Unless otherwise noted, all seminar meetings are on Thursdays at 4:00PM in Room 901 Van Vleck. Cookies and juice precede starting at about 3:45PM.
- Thursday, 21 September: What I Did Last Summer,
Group meeting
- Thursday, 28 September: Rob Owen: The Model Theory of Set Theory
- Thursday, 5 October: Will not meet.
- Thursday, 12 October: Dave Milovich: Splitting and supersplitting
- Thursday, 19 October: Asher Kach: Computable Shuffle Sums of Ordinals
- Thursday, 26 October: Open
- Thursday, 2 November: Ash Kach: Computable Model Theory
- Thursday, 9 November: Will not meet, SWLC
- Thursday, 16 November: Rob Owen, TBA
- Thursday, 23 November: Will not meet, Happy Thanksgiving!
- Thursday, 30 November: James Hunter: TBA
- Thursday, 7 December: Dilip Raghavan: TBA
- Dave Milovich, Splitting and supersplitting: I will review basic facts about splitting families of subsets of omega and introduce stronger notions of splitting, focusing on two combinatorially defined cardinals, the splitting number and the supersplitting number. The latter cardinal is closely related to some base properties of the space of free ultrafilters on omega. In the Cohen model and models of Martin's axiom, the two cardinals are equal. There are also models of set theory in which they differ.
- Asher Kach, Computable Shuffle Sums of Ordinals: In
this talk we start with some background concepts and definitions,
including computable linear orders and shuffle sums. After
demonstrating some basic properties of shuffle sums, we restrict our
attention to shuffle sums of the finite linear orders and the linear
order of order type $\omega$. By doing so, we are able to
characterize the
computable shuffle sums in terms of limit infimum sets and limitwise
monotonic sets relative to ${\bf 0}'$. As time permits, we sketch
the proof of this characterization and discuss the relationship of
these sets to the $\Sigma^0_3$ sets.
- Asher Kach, The Spectra of Computable Models of
$\aleph_1$-categorical Theories: After reviewing some fundamental
concepts of model theory, we will work through much of the paper
"Computable Models of Theories with Few Models" by Khoussainov, Nies,
and Shore. In particular, we will investigate which subsets of
$\omega + 1$ are the spectrum of computable models of an
$\aleph_1$-categorical theory. As time permits, we will work
through the proofs: both model theoretic (showing certain models are
prime or saturated) and computability theoretic (showing models are
either computable or non-computable).
- Rob Owen, Amenable Classes of L: We will prove a simple structure theorem completely characterizing amenable classes of L in the presence of 0^# in an outer model. Along the way we'll prove folklore results on indiscernibles, elementary submodels and Fodor's Lemma for Classes.