Past Seminars- Logic Set Theory

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  • Damir Dzhafarov
    Mon Oct 3, 2016
    4:00 pm
    I will discuss recent investigations of various reducibility notions between Pi^1_2 principles of second-order arithmetic, the most familiar of which is implication over the subsystem RCA_0. In many cases, such an implication is actually due to a considerably stronger reduction holding, such as a uniform (a.k.a. Weihrauch) reduction. (Here, we say...
  • Maxwell Levine
    Mon Sep 26, 2016
    4:00 pm
    Abstract: The combinatorial properties of large cardinals tend to clash with those satisfied by G\"odel's constructible universe, especially the square property (denoted $\square_\kappa$) isolated by Jensen in the seventies. Strong cardinal axioms refute the existence of square, but it is possible with some fine-tuning to produce models...
  • Omer Ben Neria
    Mon May 23, 2016
    4:00 pm
    The pursuit of better understanding the universe of set theory V motivated an extensive study of definable inner models M whose goal is to serve as good approximations to V. A common property of these inner models is that they are contained in HOD, the universe of hereditarily ordinal definable sets. Motivated by the question of how ``close"...
  • Grigor Sargsyan
    Mon May 16, 2016
    4:00 pm
    We will compute the mantle, the intersection of all grounds, of the minimal class size mouse with a Woodin cardinal and a Strong cardinal.
  • Garrett Ervin
    Mon May 9, 2016
    4:00 pm
    We complete the proof of the main theorem by showing that if X^3 is isomorphic to X, then X^{\omega} has a parity-reversing automorphism. By our previous results this implies X^2 is isomorphic to X as well. The proof generalizes to show that for any n > 1, if X^n is isomorphic to X, then X^2 is isomorphic to X. Time permitting we will discuss...
  • Dima Sinapova
    Mon May 2, 2016
    4:00 pm
    A remarkable theorem of Shelah states that if $\kappa$ is a singular strong limit cardinal of uncountable cofinality, then there is a subset $x$ of $\kappa$, such that $HOD_x$ contains the powerset of $\kappa$. We show that in general this is not  the case for countable cofinality. Using a version of diagonal supercompact extender Prikry...
  • Garrett Ervin
    Mon Apr 25, 2016
    4:00 pm
    We complete the proof of the main theorem by showing that if X^3 is isomorphic to X, then X^{\omega} has a parity-reversing automorphism. By our previous results this implies X^2 is isomorphic to X as well. The proof generalizes to show that for any n > 1, if X^n is isomorphic to X, then X^2 is isomorphic to X. Time permitting we will discuss...