Models, Algebras, and Proofs

Xavier Caicedo, Carlos Montenegro

Set theory - generic absoluteness and forcing axioms; partition of the reals and choice; analogues of the MacDowell-Specker theorem for set theory; strict genericity; weak versions of the axiom of choice for families of finite sets; heights of models of ZFC and the existence of end elementary extensions; model theory; on the (infinite) model theory of fixed point logics; stable Banach spaces and Banach space structures; induction, games, and linear orderings; query completeness, distinguishability, and rational machines. Algebraic logic - ideals in quasivarieties of algebras; amalgamation and interpolation in abstract algebraic logic; symmetric intuitionistic connectives; matrix semantics for annotated logics; twenty questions with many-valued answers; Monadic De Morgan algebras. Proof systems -inductive theorem proving in hierarchical conditional specifications; general combinatorial principles in second order bounded arithmetic; towards an information logic; standardizing the N systems of Gentzen; translations between logics.