Past Seminars- Logic Set Theory

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  • Ryan Sullivant
    Mon Mar 12, 2018
    4:00 pm
    In this talk we develop iterability theory for a single measure, give an inner model theoretic representation of 0-sharp, and show how this representation leads to non-trivial embedding of L into L.
  • Ryan Sullivant
    Mon Feb 26, 2018
    4:00 pm
    In this talk, we will continue with basics of measurable cardinals and their relationship to non-trivial elementary embeddings.  We proceed with basic facts about the constructible universe, L.  After laying this groundwork, we show L cannot have a measurable cardinal.  Time permitting, we will discuss the dichotomy introduced by...
  • Zach Norwood
    Mon Feb 12, 2018
    4:00 pm
    A major project in set theory aims to explore the connection between large cardinals and so-called generic absoluteness principles, which assert that forcing notions from a certain class cannot change the truth value of (projective, for instance) statements about the real numbers. For example, in the 80s Kunen showed that absoluteness to ccc...
  • Ryan Sullivant
    Mon Feb 5, 2018
    4:00 pm
    In this talk, we will cover the basics of measurable cardinals and their relationship to non-trivial elementary embeddings.  We proceed with basic facts about the constructible universe, L.  After laying this groundwork, we show L cannot have a measurable cardinal.  Time permitting, we will discuss the dichotomy introduced by Jensen...
  • Nam Trang
    Mon Jan 22, 2018
    4:00 am
    Forcing and elementary embeddings are central topics in set theory. Most of what set theorists have focused on are the study of forcing and elementary embeddings over models of ZFC. In this talk, we focus on forcing and elementary embeddings over models of the Axiom of Determinacy (AD). In particular, we focus on answering the following questions...
  • Sean Cox
    Mon Jan 8, 2018
    4:00 pm
    Shelah proved that a certain form of Strong Chang’s Conjecture is equivalent to the  statement ``Namba forcing is semiproper". I will present some related results about semiproperness of ``nonreasonable” posets (a notion introduced by Foreman-Magidor). This is joint work with Hiroshi Sakai.
  • Scott Cramer
    Mon Dec 4, 2017
    4:00 pm
    We will investigate algebraic structures created by rank-into-rank elementary embeddings. Our starting point will be R. Laver's theorem that any rank-into-rank embedding generates a free left-distributive algebra on one generator. We will consider extensions of this and related results. Our results will lead to some surprisingly coherent...