Richard A. Shore : Publications
Curriculum Vitae
Most of the documents below with electronic versions have been compiled for optimum
viewing in PDF format. However, some papers (for various reasons) look
grainy as PDF files. All the papers with electronic versions are, however, also
available
in postscript and DVI format.
 On large cardinals and partition relations, Journal of Symbolic Logic
36 (1971), 305308 (with E.M. Kleinberg).
 Weak compactness and square bracket partition relations, Journal of
Symbolic Logic 37 (1972), 673676 (with E.M. Kleinberg).
 Square bracket partition relations in L, Fundamenta Mathematica
34 (1974), 101106.
 Minimal alphadegrees, Annals of Mathematical Logic 4
(1972), 383414.
 Cohesive sets: countable and uncountable, Proceedings of the
American Mathematical Society 44 (1974), 442445.
 Sigma_{n} sets which are Delta_{n}incomparable
(uniformly), Journal of Symbolic Logic 39 (1974), 295304.
 Splitting an alpharecursively enumerable set, Transactions of the American
Mathematical Society 204 (1975), 6577.
 The recursively enumerable alphadegrees are dense, Annals of
Mathematical Logic 9 (1976), 123155.
 The irregular and nonhyperregular alphar.e. degrees, Israel
Journal of Mathematics 22 (1975), 2841.
 On the jump of an alpharecursively enumerable set,
Transactions of the American Mathematical Society 217 (1976), 351363.
 Types of simple alpharecursively enumerable sets, Journal of
Symbolic Logic 41 (1976), 681693 (with A. Leggett).
 alphaRecursion theory, in Handbook of Mathematical Logic, J.Barwise ed.,
NorthHolland, 1977, 653680.
 Determining automorphisms of the recursively enumerable sets,
Proceedings of the American Mathematical Society 65 (1977), 318325.
 Controlling the dependence degree of a recursively enumerable vector
space, Journal of Symbolic Logic 43 (1978), 1322.
 Some more minimal pairs of alpharecursively enumerable degrees,
Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik
24 (1978), 409418.
 Nowhere simple sets and the lattice of recursively enumerable sets,
Journal of Symbolic Logic 43 (1978), 322330.
 On the AEsentences of alpharecursion theory, in
Generalized Recursion Theory II, Fenstad, Gandy and Sacks, eds.,
NorthHolland 1978, 331354.
 rMaximal major subsets, Israel Journal of Mathematics 31
(1978), 118 (with M. Lerman and R.I. Soare).
 Second order logic and first order theories of reducibility orderings in
The Kleene Symposium, J. Barwise, H.J. Keisler and K. Kunen, eds.,
North Holland, 1980, 181200 (with A. Nerode).
 Reducibility orderings: theories, definability and automorphisms,
Annals of Mathematical Logic 18 (1980), 6189 (with A. Nerode).
 The homogeneity conjecture, Proceedings of the National Academy of
Sciences 76 (1979), 42184219.
 On homogeneity and definability in the first order theory of the Turing
degrees, Journal of Symbolic Logic 47 (1982), 816.
 L^{*}(K) and other lattices of recursively enumerable sets,
Proceedings of the American Mathematical Society 80 (1980),
143146.
 Some constructions in alpharecursion theory, in Recursion
Theory: Its Generalizations and Applications, F.R. Drake and S.J. Wainer,
eds., London Mathematical Society Lecture Notes Series, no. 45, Cambridge
University Press, Cambridge, England, 1980, 158170.
 The theory of the degrees below 0', Journal of the
London Mathematical Society 24 (1981), 114.
 The elementary theory of the recursively enumerable degrees is not
aleph_{0}categorical, Advances in Mathematics 53 (1984),
301320 (with M. Lerman and R.I. Soare).
 Splitting properties and jump classes, Israel Journal of Mathematics
39 (1981), 210224 (with W. Maass and M. Stob).
 Definable degrees and automorphisms of D, Bulletin of the
American Mathematical Society (NS) 4 (1981), 97100
(with L. Harrington).
 The degrees of unsolvability: global results, in Logic Year
198081: The University of Connecticut, M. Lerman, J. Schmerl and R. Soare,
eds., Springer Verlag, 1981, 283301.
 Finitely generated codings and the degrees r.e. in a degree d,
Proceedings of the American Mathematical Society 84 (1982), 256263.
 The Turing and truthtable degrees are not elementarily equivalent, in
Logic Colloquium 1980, D. van Dalen, D. Lascar and T.J. Smiley, eds.,
NorthHolland, Amsterdam 1982, 231237.
 An algebraic decomposition of the recursively enumerable degrees and the
coincidence of several degree classes with the promptly simple degrees,
Transactions of the American Mathematical Society 281 (1984), 109128
(with K. AmbosSpies, C. Jockusch and R. Soare).
 Pseudojump operators I: the r.e. case, Transactions of the
American Mathematical Society 275 (1983), 599610 (with C. Jockusch).
 Pseudojump operators II: transfinite iterations hierarchies and minimal
covers, Journal of Symbolic Logic 49 (1984), 12051236 (with C.
Jockusch).
 The arithmetical degrees are not elementarily equivalent to the Turing
degrees, Archiv fur Mathematische Logik und Grundlagenforschung
24 (1984), 137139.
 The degrees of unsolvability: the ordering of functions by relative
computability, in Proceedings of the International Congress of
Mathematicians (Warsaw) 1983, PWNPolish Scientific Publishers, Warsaw
1984, Vol. 1, 337346.
 Recursion Theory, Proceedings of the Symposia in Pure Mathematics,
Vol. 42 (Proceedings of the AMSASL Summer Institute on Recursion Theory,
Cornell, 1982), American Mathematical Society, Providence, R.I., 1985
(edited with A. Nerode).
 The structure of the degrees of unsolvability, in Recursion Theory,
Proceedings of the Symposia in Pure Mathematics 42, A. Nerode and
R.A. Shore, eds., American Mathematical Society,Providence, R.I., 1985,
3351.
 REA operators, r.e. degrees and minimal covers, in Recursion
Theory, Proceedings of the Symposia in Pure Mathematics 42, A. Nerode
and R.A. Shore, eds., American Mathematical Society,Providence, R.I., 1985,
311 (with C. Jockusch).
 Embeddings and extensions of embeddings in the r.e. tt and wtt
degrees, in Proceedings of the Oberwolfach "Recursion Theoretic Week
1984", H.D. Ebbinghaus, G.H. Müller and G.E. Sacks, eds.,
SpringerVerlag, Berlin, 1985, 121140 (with P. Fejer).
 Recursive limits on the HahnBanach theorem, Contemporary
Mathematics 39 (1985), 8591 (with A. Nerode and G. Metakides).
 Initial segments of the Turing degrees of size aleph_{1},
Israel Journal of Mathematics 55 (1986), 151 (with U. Abraham).
 The degrees of constructibility below a Cohen real, Journal of the
London Mathematical Society (3) 53 (1986), 193208 (with U. Abraham).
 Infima of recursively enumerable truth table degrees, Notre Dame
Journal of Formal Logic 29 (1988), 420437 (with P. Fejer).
 A noninversion theorem for the jump operator, Annals of Pure and
Applied Logic 40 (1988), 277303.
 Decidability and invariant classes for degree structures,
Transactions of the American Mathematical Society 310 (1988), 669692
(with M. Lerman).
 Defining jump classes in the degrees below 0',
Proceedings of the American Mathematical Society 104 (1988), 287292.
 Initial segments of the degrees of constructibility, Israel Journal
of Mathematics, Israel Journal of Mathematics 63 (1988), 149177
(with M. Groszek).
 The pTdegrees of the recursive sets: lattice embeddings, extension
of embeddings and the two quantifier theory (extended abstract), in
Proceedings: Structures in Complexity Theory, 4^{th} Annual Conference,
Comp. Soc. IEEE, 1989 (with T. Slaman).
 A direct construction of a minimal recursively enumerable truthtable
degree, in Recursion Theory Week, Proceedings Oberwolfach 1989, K.
AmbosSpies, G. H. Muller and G. E. Sacks, eds. SpringerVerlag, LNMS
1432 (1990), 187204 (with P. Fejer).
 Undecidability and initial segments of the (r.e.) ttdegrees,
Journal of Symbolic Logic 55 (1990), 9871006 (with C. Haught).
 Working below a low_{2} recursively enumerable degrees, Archive for
Mathematical Logic 29 (1990), 201211 (with T. Slaman).
 Undecidability and initial segments of the wttdegrees below 0',
in Recursion Theory Week, Proceedings Oberwolfach 1989, K. AmbosSpies,
G. H. Muller and G. E. Sacks, eds. SpringerVerlag, LNMS
1432 (1990), 223244 (with C. Haught).
 Global properties of local structures of degrees, Bul. U. Mat. Ital.
7 (1991), 97120 (with G. Odifreddi).
 On the strength of König's duality theorem for infinite bipartite
graphs, Journal of Combinatorial Theory (B) 54 (1992), 257290
(with R. Aharoni and M. Magidor).
 The pTdegrees of the recursive sets: lattice embeddings, extension
of embeddings and the two quantifier theory, Theoretical Computer
Science 97 (1992), 263284 (with T. Slaman).
 Working below a high recursively enumerable degree, Journal of
Symbolic Logic 58 (1993), 824859 (with T. Slaman).
 Degrees of constructibility, in Set theory of the Continuum, H.
Judah, W. Just and H. Woodin eds., MSRI Publications 26,
SpringerVerlag, Berlin, 1992, 123135.
 The nr.e.a. enumeration degrees are dense, Archive for
Mathematical Logic 31(1992), 227285 (with A. Lachlan).
 The theory of the recursively enumerable weak truth table degrees is
undecidable, Journal of Symbolic Logic 57 (1992), 864874 (with
AmbosSpies and Nies).
 Countable thin Pi_{1}^{0}
classes, Annals of Pure and Applied Logic 59 (1993)
79139 (with D. Cenzer, R. Downey and C. Jockusch).
Also available in
postscript
or
DVI
format.
 Undecidability and 1types in the r.e. degrees, Annals of Pure
and Applied Logic 63 (1993), 337 (with K. AmbosSpies).
 On the strength of Fraïssé's conjecture, in Logical Methods,
J. N. C. Crossley, J. Remmel, R. A. Shore and M. Sweedler, eds.,
Birkhäuser, Boston, 1993, 782813.
 Interpreting true arithmetic in the theory of the r.e. truth table
degrees, Annals of Pure and Applied Logic, 75 (1995), 269311
(with A. Nies).
 Degree theoretic definitions of the
low_{2} r. e. sets, Journal of Symbolic Logic 60
(1995), 727756 (with R. Downey).
Also available in
postscript
or
DVI
format.
 Jumps of minimal degrees below 0',
Journal of the London Mathematical Society 60 (1995), 727756
(with R. Downey and S. Lempp).
Also available in
postscript
or
DVI
format.
 Highness and bounding minimal pairs,
Mathematical Logic Quarterly 39 (1993), 475491 (with R.
Downey and S. Lempp)
Also available in
postscript
or
DVI
format.
 The theories of the T, tt and wtt r.e.
degrees: undecidability and beyond, in Proc. IX Latin American Symposium
on Mathematical Logic (part 1), Notas de Lo'gica Mathema'tica 38,
Universidad Nacional del Sur, Bahia Blanca, Argentina, 1993, 6170.
Also available in
postscript
or
DVI
format.
 Logical Methods: In Honor of Anil Nerode's Sixtieth Birthday,
Birkäuser, Boston, Mass., 1993 (edited with J. N. C. Crossley, J. Remmel
and M. Sweedler).
 Logic for Applications, Texts and Monographs in Computer Science,
SpringerVerlag, New York, 1993 (with A. Nerode); 2^{nd} ed., Graduate
Texts in Computer Science, SpringerVerlag, New York, 1997 (with A. Nerode).
 Conjectures and questions from Gerald
Sacks's Degrees of Unsolvability, Archive for Mathematical
Logic 36 (1997), 233253.
Also available in
postscript
or
DVI
format.
 Lattice embeddings below a
nonlow_{2} recursively enumerable degree,
Israel Journal of Mathematics 94 (1996), 221246
(with R. Downey).
Also available in
postscript
or
DVI
format.
 Interpolating dr.e. and REA degrees between
r.e. degrees, Annals of Pure and Applied Logic 78 (1996),
2956 (with M. Arslanov and S. Lempp).
Also available in
postscript
or
DVI
format.
 On isolating r.e. and isolated dr.e.
degrees, in Computability, Enumerability, Unsolvability: Directions in
Recursion Theory, S. B. Cooper, T. A. Slaman and S. S. Wainer eds.,
LMSLN 224, Cambridge University Press, Cambridge, England,
1996, 6180 (with M. Arslanov and S. Lempp).
Also available in
postscript
or
DVI
format.
 The recursively enumerable degrees,
in Handbook of Recursion Theory, E. Griffor ed., NorthHolland,
Amsterdam, 1999, 169197.
Also available in
postscript
or
DVI
format.
 Intervals without critical triples,
in Logic Colloquium '95, J.
A. Makowsky and E. V. Ravve, eds., Lecture Notes in Logic 11,
SpringerVerlag, Heidelberg, 1998, 1743 (with P. Cholak and R. Downey).
Also available in
postscript
or
DVI
format.
 Definability in the recursively enumerable degrees, Bulletin of Symbolic
Logic 2 (1996), 392404, (with A. Nies and T. Slaman).
Also available in
postscript
or
DVI
format.
 Computably categorical structures and
extensions by constants, Journal of Symbolic Logic, 64 (1999), 1337 (with P. Cholak, S. Goncharov and B.
Khoussainov).
Also available in
postscript
or
DVI
format.
 Computable models of theories with few
models, Notre Dame Journal of Formal Logic 38 (1997),
165178 (with B. Khoussainov and A. Nies).
Also available in
postscript
or
DVI
format.
 Splitting theorems and the jump operator,
Annals of Pure and Applied Logic 94 (1997), 4552 (with R. Downey).
Also available in
postscript
or
DVI
format.
 There is no degree invariant half jump,
Proc. Am Math. Soc. 125 (1997), 30333037 (with R. Downey).
Also available in
postscript
or
DVI
format.
 Categoricity and Scott families,
extended abstract, Combinatorics, Complexity and Logic, Proceedings of DMTCS
'96, D. Bridges et al. eds., SpringerVerlag, Singapore, 1997, 299308 (with B. Khoussainov).
Also available in
postscript
or
DVI
format.
 Interpretability and definability in the
recursively enumerable degrees, Proc. Lon. Math. Soc. (3) 77
(1998), 241291 (with A. Nies and T. Slaman).
Also available in
postscript
or
DVI
format.
 Computable Isomorphisms, Degree Spectra of
Relations, and Scott Families, Annals of Pure and Applied Logic
93 (1998), 153193 (with B. Khoussainov).
Also available in
postscript
or
DVI
format.
Revised version in
postscript
or
DVI
format.
 Undecidability and 1types in
intervals of the c.e. degrees, Annals of Pure and Applied Logic
106 (2000), 148 (with K. AmbosSpies and D. Hirschfeldt).
Also available in
postscript
or
DVI
format.
 Jumps of Sigma2high edegrees
and properly Sigma2 edegrees, in Recursion Theory and Complexity, M. Arslanov and S. Lempp
eds., de Gruyter Series in Logic and its Applications 2, de Gruyter,
Berlin, 1999, 157172 (with A. Sorbi).
Also available in
postscript
or
DVI
format.
 Effective model theory: the number of models
and their compelxity, in
Models and Computability, Invited papers from Logic Colloquium '97, S.
B. Cooper and J. K. Truss eds., LMSLNS 259, Cambridge University
Press, Cambridge, England, 1999, 193240 (with B. Khoussainov).
Also available in
postscript
or
DVI
format.
 Every incomplete computably enumerable truthtable degree is branching,
Archive for Mathematical Logic 40 (2001), 113123 (with P. Fejer).
Also available in
postscript
or
DVI
format.
 Reasoning about common knowledge with infinitely many agents,
Information and Computation 191 (2004), 140 (with J. Halpern).
Also available in
postscript as is the
Extended abstract
from the Proceedeings of LICS Meeting, Trento, Italy, July 1999
or
DVI as is the
Extended abstract
from the Proceedeings of LICS Meeting, Trento, Italy, July 1999.
 Solutions of the GoncharovMillar and degree spectra problems in the
theory of computable models, Dokl. Akad. Nauk SSSR
371 (2000) 3031 (Russian), English version: Doklady Mathematics
61 (2000), 178179 (with B. Khoussainov).
Also available in
postscript
or
DVI
format.
 Decomposition and infima in the
computably enumerable degrees, Journal of Symbolic Logic,
68 (2003), 551579 (with R. Downey and G. Laforte).
Also available in
postscript
or
DVI
format.
 Degree spectra and computable dimension
in algebraic structures,
Annals of Pure and Applied Logic
115 (2002), 71113 (with D. Hirschfeldt, B. Khoussainov and A. Slinko).
Also available in
postscript
or
DVI
format.
 Natural definability in degree
structures, in Computability Theory
and Its Applications: Current Trends and Open Problems, P. Cholak, S. Lempp,
M. Lerman and R. A. Shore eds., Contemporary Mathematics, AMS,
Providence RI, 2000, 255272.
Also available in
postscript
or
DVI
format.
 A splitting theorem for
nREA degrees, Proc. American
Mathematicl Society 129 (2001), 37213728 (with T. Slaman).
Also available in
postscript
or
DVI
format.
A follow up paper is A discrete splitting theorem for the
2REA degrees (with T. Slaman).
Also available in
postscript
or
DVI
format.
 Defining the Turing jump,
Math. Research Letters 6 (1999), 711722 (with T. Slaman).
Also available in
postscript
or
DVI
format.
 Computability Theory and Its Applications: Current Trends and
Open Problems, Contemporary Mathematics, AMS, Providence RI,
2000 (edited with P. Cholak, S. Lempp and M. Lerman).
 Computable Structures: Presentations Matter,
in In the scope of logic, methodology and the philosophy of science},
Int. Congress of LMPS, Cracow, August 1999, P. Gardenfors, J. Wolenski and
K. KijaniaPlacek eds., Synthese Library 315, Kluwer Academic Publishers,
Dordrecht, 2002, vol. 1, 8195.
Also available in
postscript
or
DVI
format.
 A nonlow_{2} r.e. degree with
the extension of embeddings properties of a low_{2} degree,
Mathematical Logic Quarterly 6 (2002), no. 1
(with Y. Yang).
Also available in
postscript
or
DVI
 Intepreting arithmetic in the
r.e. degrees under ISigma4induction, in Reverse Mathematics 2001,
S. Simpson, ed., Lecture Notes in Logic 21, Association for Symbolic Logic, 2005
(with C. T. Chong and Y. Yang).
 The prospects for mathematical
logic in the twentyfirst century, Bulletin of Symbolic Logic
7 (2001), 169196 (with S. Buss, A. Kechris and A. Pillay).
Also available in
postscript
or
DVI
format.
 The theory of the metarecursively enumerable
degrees, Journal of
Mathematical Logic, 6 (2006), 4968 (with T. Slaman and N. Greenberg).
Also available in
postscript
or
DVI
format.
 A computably categorical
structure whose expansion by a constant has infinite computable dimension,
Journal of Symbolic Logic 68 (2003), 11991241
(with D. Hirschfeldt and B. Khoussainov).
Also available in
postscript
or
DVI
format.
 Undecidability of the AEtheory of $\mathcal{R}(\leq
,\vee ,\wedge ), Transactions of the American Mathematical Society,
356 (2004), 30253067 (with A. Nies and R. Miller).
Also available in
postscript
or
DVI
 Minimal degrees which are
Sigma_2 but not Delta_2, Proc. American
Mathematicl Society 132 (2004), 563565.
Also available in
postscript
or
DVI
format.
 Pi^1_1 relations and paths
through O, Journal of Symbolic Logic 69 (2004), 585611
(with S.S. Goncharov, V. Harizanov and J. Knight).
Also available in
postscript
or
DVI
format.
 The AE theory of
$\mathcal{D}(\leq ,\vee ,^{\prime })$ is undecidable,
in Logic Colloquium '03, Viggo StoltenbergHansen and Jouko Vaananen eds.,
Lecture Notes in Logic 24, ASL, ASL, 2006, 326344 (with T.A. Slaman).
Also available in
postscript
or
DVI
format.
 Generalized high degrees have the
complementatation property, Journal of Symbolic Logic 69
(2004), 12001220 (with N. Greenberg and A. Montalban).
Also available in
postscript
or
DVI
format.
 Invariants, Boolean algebras and ACA_0^+ ,
Transactions of the American Mathematical Society, 358 (2006), 9891014.
Also available in
postscript
or
DVI
format.
 A computably stable structure with no Scott family of finitary
formulas, Archive for Mathematical Logic, 45 (2006), 519538
(with P. Cholak and R. Solomon).
Also available in
postscript
or
DVI
format.
 Boolean Algebras,
Tarski Invariants, and Index Sets , Notre Dame
Journal of Formal Logic, 47 (2006), 123
(with B. Csima and A. Montalban).
Also available in
postscript
or
DVI
format.
 The lown and lowm r.e. degrees are not
elementarily equivalent, Science in China AMathematics, 47
(2004), 950956.
Also available in
postscript
or
DVI
format.
 Rigidity
and biinterpretability in the hyperdegrees, in Recursion
Theory Worksphop:Proceedings of the IMS Program, Computational Prospects of
Infinity, C. T. Chong , F. Qi and Y. Yang eds., World Scientific Publishing
Co., Singapore, 2008, 299312.
Also available in
postscript
or
DVI
format.
 Combinatorial principles weaker than Ramsey's
theorem for pairs, Journal of Symbolic Logic 72 (2007),
171206 (with D. Hirschfeldt).
Also available in
postscript
or
DVI
format.
 Degree Structures:
Local and Global Investigations, Bulletin of Symbolic Logic,
12 (2006), 369389.
Also available in
postscript
or
DVI
format.
 The settlingtime reducibility ordering,
Journal of Symbolic Logic, 72 (2007), 105571 (with B. Csima).
Also available in
postscript
or
DVI
format.
 Direct and local defintions of the Turing
jump, Journal of Mathematical Logic 7 (2007), 229262.
Also available in
postscript
or
DVI
format.
 Local definability in degree structures:
the Turing jump, hyperdegrees and beyond, Bulletin of Symbolic Logic,
13 (2007), 226239.
Also available in
postscript
or
DVI
format.
 Lattice initial segments of the hyperdegrees,
Journal of Symbolic Logic 75 (2010), 103 130 (with B. KjosHanssen).
Also available in
postscript
or
DVI
format.
 The atomic model theorem,
Transactions of the American Mathematical Society,
361 (2009), 58055837 (with D. Hirschfeldt and T. Slaman).
Also available in
postscript
or
DVI
format.
 Domination, forcing, array nonrecursiveness and
relative recursive enumerability,
Journal of Symbolic Logic, 77 (2012), 226239 (with M. Cai).
Also available in
postscript
DVI
format.
 Reverse mathematics, countable
and uncountable: a computational approach, Effective Mathematics of the
Uncountable, D. Hirschfeldt, N. Greenbergm J. D. Hamkins and R. Miller, eds.,
Lecture Notes in Logic, ASL and Cambridge University Press, New York,
2013, 150163.
Also available in
postscript
or
DVI
format.
 Topological aspects of
the Medvedev lattice, Archive for
Mathematical Logic 50 (2011), 319340 (with A. E. M. Lewis and A. Sorbi).
Also available in
postscript
or
DVI
format.
 The limits of determinacy in second
order arithmetic Proceedings of the London Mathematical Society,
104 (3) (2012), 223252 (with A. Montalban).
Also available in
postscript
or
DVI
format.
 Reverse Mathematics: the Playground of Logic,
Bulletin of Symbolic Logic 16 (2010), 378402.
Also available in
postscript
or
DVI
format.

The nr.e. degrees: undecidability and $\Sigma _{1}$ substructures,
Journal of Mathematical Logic, 12 (2012), 130 (with M. Cai and T. Slaman).
Also available in
postscript
or
DVI
format.

The maximal linear extension theorem in second order arithmetic,
Archive for Mathematical Logic 50 (2011), 543564 (with A. Marcone).
Also available in
postscript
or
DVI
format.

Degrees of categoricity and the hyperarithmetic hierarchy,
Notre Dame Journal of Formal Logic, 54 (2012), 215232 (with B. F. Csima and J. Y. N. Franklin).
Also available in
postscript

Computably enumerable partial orders,
Computability, 1 (2012), 99107 (with P. A. Cholak, D. D. Dzhafarov and N. Schweber).
Also available in
postscript
or
DVI
format.

Biinterpretability up to double jump
in the degrees below 0',
Proceedings of the American Mathematical Society, 142 (2014), 351360.
Also available in
postscript
or
DVI format.

The Turing Degrees: An Introduction, in Forcing, Iterated Ultrapowers, and Turing
Degrees, Lecture Notes Series, Institute for Mathematical Sciences, National University of
Singapore 29, eds. Chong Chi Tat, Feng Qi, Yang Yue, Theodore Slaman and Hugh Woodin,
World Scientific Publishing, 2015, 39121.
Also available in
postscript
or
DVI format.

Computing maximal chains,
Archive for Mathematical Logic 51 (2012), 651660 (with A. Marcone and A. Montalban).
Also available in
postscript
or
DVI format.

The complexity of ascendant sequences in locally nilpotent groups,
International Journal of Algebra and Computation 24 (2014), 189205 (with C. Conidis).
Also available in
DVI format.

Low level nondefinability results: domination and recursive enumeration,
Journal of Symbolic Logic 78 (2013), 10051024 (with M. Cai).
Also available in
postscript
or
DVI format.

The Turing degrees below generics and randoms,
Journal of Symbolic Logic, 79 (2014), 171178.
Also available in
postscript
or
DVI format.

The Limits of Determinacy in Second Order Arithmetic:
Consistency and Complexity Strength,
Israel Journal of Mathematics, 204 (2014), 477508 (with A. Montalban).
Also available in
postscript
or
DVI format.

The Strength of Turing Determinacy within Second Order Arithmetic,
Fundamenta Mathematica, 232 (2016), 249268 (with A. Montalban).
Also available in
postscript
or
DVI format.

Induction, Bounding,
Weak Combinatorial Principles,
and The Homogeneous Model Theorem,
Memoirs of the American Mathemactial Society 249,
American Mathematical Society, Providence, R.I. 2107, vi + 101
(with D. Hirschfeldt and K. Lange).
Also available in
postscript
or
DVI format.

On the jumps of the degrees below an r.e. degree,
Notre Dame Journal of Formal Logic to appear (with D. Belanger).
Also available in
postscript
or
DVI format.

The strength of the GraetzerSchmidt theorem,
Archive for Mathematical Logic, 55 (2016), 687704 (with K. Brodhead, M. Khan,
B. KjosHansen, W A. Lampe and K. L. V. Nguyen).
Also available in
postscript
or
DVI format.

Mass problems and density,
Journal of Mathematical Logic 16 (2016), 1650006 (with S. Binns and S. Simpson).
Also available in
postscript
or
DVI format.

Sigma ^1_1 in every real in a Sigma ^1_1 class of reals
is Sigma ^1_1, in
Computability and Complexity, Essays Dedicated to Rodney Downey on the
Occasion of His 60th Birthday,
A. Day, M. Fellows, N. Greenberg, B. Khoussainov, A. Melnikov and F. Rosamond eds.,
SpringerVerlag, 2017, 455468 (with L. Harrington and T. A. Slaman).
Also available in
postscript
or
DVI format.

Conservativity of ultrafilters over subsystems of second order arithmetic,
Journal of Symbolic Logic,
83 (2018), 740765 (with A. Montalban).
Also available in
postscript
or
DVI format.
 Logic, Mathematics, Computer Science, in The Art and Practice of Mathematics, Interviews at
the Institute for Mathematical Sciences, National University of Singapore, 20102020, Yu Kiang Leong,
World Scientific, Singapore, 2021, 268281.
 Type omitting theorems for fragments of second
order logics: classical and modal,
to appear.

Theorems of hyperarithmetic analysis and almost theorems of hyperarithmetic analysis,
Bulletin of Symbolic Logic 28 (2022), 133149 (with J. Barnes and J. L. Goh).

Halin's infinite ray theorems: complexity and reverse mathmematics: Version E,
to appear (with J. Barnes and J. L. Goh).

Almost theorems of hyperarithmetic analysis,
Journal of Symbolic Logic, 88 (2023), 664696.
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