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, Jan. 24: David Milovich, Noetherian types of oredered compacta
- Thursday, Feb. 14: Gabriel Pretel, Model theory of modules
- Thursday, Feb. 14: Gabriel Pretel, Model theory of modules II
- Thursday, Feb. 21: Gabriel Pretel, Model theory of modules III
- Thursday, Mar. 6: Andrea Medini, Non-isomorphic hyperreal fields
- Thursday, Mar. 27: Dan Rosendorf, Iterated forcing and m < c
- Thursday, Apr. 3: Dan Rosendorf, Iterated forcing and m < c, part II
- Thursday, Apr. 10: Dilip Raghavan, On a Conjecture of J. Brendle
- Thursday, Apr. 24: Ben Ellison, Lindstrom's Theorem, or How I Learned to Stop Worrying and Love First Order Logic.
- Thursday, May 1: Ben Ellison, Lindstrom's Theorem, part II.
- Thursday, May 8: David Milovich, Omega_1 is special: Hausdorff gaps and Luzin families
David Milovich, Noetherian types of oredered compacta
The Noetherian type of a space X is the least infinite cardinal kappa such that X has a base of open sets such no open set has kappa-many basic supersets. There is a compact linear order with Noetherian type kappa if and only if kappa is not omega_1 and kappa is not weakly inaccessible.
Andrea Medini, Non-isomorphic hyperreal fields
I will talk about Roitman's paper, "Non-isomorphic hyperreal fields from
non-isomorphic ultrapowers", where she
shows it's consistent to have c many
hyperreal fields of size c.
Dilip Raghavan, On a Conjecture of J. Brendle
In 2006 Brendle conjectured that if cov(M) < a_e, there are no very MAD families. We will prove Brendle's conjecture. Our theorem implies that there are no very MAD families in the Laver or the Random model. We will assume some familiarity with cardinal invariants of the continuum.
Benjamin Ellison, Lindstrom's Theorem, or How I Learned to Stop Worrying and Love First Order Logic.
First order logic is almost always the framework we use when doing math. Why don't we use any other logical system? In this talk, I will discuss and prove Lindstrom's theorem, which tells us that if we want to use a different style of logic, we sacrafice some important property that first order logic has. I will also mention some other types of logic, and what properties they lack.
David Milovich, omega_1 is special: Hausdorff gaps and Luzin families
Martin's Axiom implies that all uncountable sets of reals of size less than c are in many ways just as small as countable sets. Hausdorff gaps and Luzin families are omega_1-sized sets of reals that are strong counterexamples to this pattern. I will describe these objects and present their elementary ZFC constructions.