Logic Seminar

Romin AbdolahzadiCornell University
Stability Theory and Nonforking

Tuesday, December 15, 2020 - 3:00pm
Zoom meeting 922 0989 3006

Last time we introduced the notion of a freeness relation for types over parameter sets, generalizing linear and algebraic independence. We ended by showing that If $T$ admits a freeness relation satisfying the axioms, increasing chains of saturated models of $T$ remain saturated. Now we introduce stable model theory whose paradigm is of the form ``many types implies many models; few types implies few models'' wherein ``few models'' is tantamount to ``admits a structure theory''. Within the context of the last talk this means ``admits a freeness relation satisfying our axioms'', and we show that every stable theory admits such a relation known as nonforking - this leads to a division of all first-order theories into four classes: unstable, stable, superstable, and $\omega$-stable.