This semester the topic component to the logic seminar will focus on topics related to proper forcing. The papers presented in this part of the seminar are grouped into clusters, with some background presented leading up to the main result.

The following references provide background and motivation on proper forcing:

S. Shelah, __Proper and Improper Forcing__, *2nd edition. Perspectives in Mathematical Logic, Volume 5
Springer-Verlag: Berlin (1998), 1020 pp.* This is the original source on proper forcing.

J. Tatch Moore, A tutorial on the Proper Forcing Axiom
* 2010 Young Set Theory Meeting, Raach, Austria (notes by Giorgio Venturi). *
This contains the basics on applying the proper forcing axiom, complete with proofs that PFA implies OCA and PID.

J. Tatch Moore,
The Proper Forcing Axiom
* Proceedings of the 2010 meeting of the ICM. pp. 3--29* This is an expository article, motivating
the proper forcing axiom.

T. Eisworth, D. Milovich, J. Tatch Moore,
Iterated forcing and the Continuum Hypothesis
in *Appalachian set theory 2006-2012, J. Cummings and E. Schimmerling, eds.
London Math Society Lecture Notes series, Cambridge University Press (2013).*
This contains a proof that a countable support iteration of proper forcings is proper.
It also contains information on obtaining models of CH by iterated proper forcing.

The first pair of papers which will be presented in the seminar will be:

[M1] J. Tatch Moore, Set mapping reflection
* Journal of Mathematical Logic, *
** 5 **
(2005), n 1, pp. 87-98.

[IM] T. Ishiu, J. Tatch Moore, Minimality of non \(\sigma\)-scattered orders
* Fundamenta Mathematicae. *
** 205 ** (2009), n 1, pp. 29--44.

The following contains some additional reading:
D. Milovich, J. Moore,
A tutorial on Set Mapping Reflection
in *Appalachian set theory 2006-2012,* J. Cummings and E. Schimmerling, eds.
London Math Society Lecture Notes series, Cambridge University Press (2013).

The second cluster will some introductory material on iterating proper forcing without adding reals
(see AST notes for the Eisworth-Moore tutorial above) followed by:

[M2] J. Tatch Moore,
\(\omega_1\) and \(-\omega_1\) may be the only minimal uncountable order types
* Michigan Math. Journal *
** 55 ** (2007), n 2, pp. 437--457.

**Fall 2013 talks:**

Tuesday, 9/3: *Brooks' theorem on standard probability spaces*

**Clinton Conley**, Cornell University

Wednesday, 9/4: * no seminar (fall reception)*

Tuesday, 9/10: *Brooks' theorem on standard probability spaces, part II*

**Clinton Conley**, Cornell University

Wednesday, 9/11: * An introduction to proper forcing*

** Justin Moore**, Cornell University

Tuesday, 9/17: (canceled)

Wednesday, 9/18: * An introduction to proper forcing, part II*

** Justin Moore**, Cornell University

Tuesday, 9/24: *Finite forms of Gowers' Theorem on the oscillation stability of \(c_0\)
Diana Ojeda, Cornell University
Wednesday, 9/25: Iterated proper forcing
Justin Moore, Cornell University
Tuesday, 10/1: Saturated models and disjunctions in second-order arithmetic
David Belanger, Cornell University
Wednesday, 10/2: Set Mapping Reflection
David Belanger, Cornell University
Tuesday, 10/8: TBA
Adam Bjorndahl, Cornell University
Wednesday, 10/9: Minimal non \(\sigma\)-scattered linear orders
Hossein Lamei Ramandi, Cornell University
Tuesday, 10/15: no seminar (fall break)
Wednesday, 10/16: Minimal non \(\sigma\)-scattered linear orders, part II
Hossein Lamei Ramandi, Cornell University
Tuesday, 10/22: Devlin and Shelah's weak diamond principle
Jeffrey Bergfalk, Cornell University
Wednesday, 10/23: Games and Borel graph colorings
Andrew Marks, Caltech
Tuesday, 10/29: Continuous automata over a compact alphabet
Scott Messick, Cornell University
Wednesday, 10/30: Introduction to iterated totally proper forcing
Justin Moore, Cornell University
Tuesday, 11/5: The Open Coloring Axiom
Iian Symthe, Cornell University
Wednesday, 11/6: \(\omega_1\) and \(-\omega_1\) may be the only minimal
uncountable linear orders
Jeffrey Bergfalk, Cornell University
Tuesday, 11/12: PFA and automorphsisms of \(\mathcal{P}(\mathbb{N})/\mathrm{fin}\), part I
Iian Smythe, Cornell University
Wednesday, 11/13: \(\omega_1\) and \(-\omega_1\) may be the only minimal
uncountable linear orders, part II
Jeffrey Bergfalk, Cornell University
Tuesday, 11/19: The P-ideal Dichotomy
Diana Ojeda, Cornell University
Wednesday, 11/20: PFA implies PID
Justin Moore, Cornell University
Tuesday, 11/26: PFA implies OCA
Iian Smythe, Cornell University
Wednesday, 11/27: no seminar (Thanksgiving break)
Tuesday, 12/3: Memoryless determinacy of parity games
Tom Kern, Cornell University
Wednesday, 12/4: The consistency of the Proper Forcing Axiom, part I
Scott Messick, Cornell University
Wednesday, 12/11: The consistency of the Proper Forcing Axiom, part II
Scott Messick, Cornell University
Thursday, 12/12: Linear orders \(L\) satisfying \(L^n = L\)
Garrett Ervin, University of California, Irvine
*