7-8 April 2010, Set theory seminar.

We are having an informal set theory seminar. Anyone who is interested in set theory is welcome to attend.

Programme:

Wednesday, 7 April, 14:00 - 17:00 hrs (@C1.112)
14:00-15:20 Juliette Kennedy
15:20-15:30 break
15:30-16:50 Jouko Väänänen

Thursday, 8 April, 14:00 - 17:00 hrs (@A1.08)
14:00-14:50 Brian Semmes
14:50-15:00 break
15:00-15:50 Lauri Keskinen
15:50-16:00 break
16:00-16:50 Daisuke Ikegami

Location:

Science Park Amsterdam
Science Park 904
1098 XH Amsterdam
Rooms: C1.112 (Wed.) & A1.08 (Thu.)

Titles and abstracts:

Daisuke Ikegami: AD_R and Bl-AD_R.
We compare the Axiom of Real Determinacy (AD_R) and the Axiom of Real Blackwell Determinacy (Bl-AD_R). We give several results towards the equivalence between AD_R and Bl-AD_R under ZF+DC. This is a joint work with W. Hugh Woodin.

Juliette Kennedy: On a Finitary Square Principle.
We discuss some (classical) model-theoretic equivalents of a finite square principle. This is joint work with Saharon Shelah and Jouko Väänänen.

Lauri Keskinen: Characterizing all models up to isomorphism in cardinality kappa.
My talk is about possibility of characterizing all models of cardinality kappa in any finite vocabulary up to isomorphism by their theories in certain infinitary second order languages.

Brian Semmes: Tree representations for Baire class alpha.
I cover recent progress of Louveau, extending the "tree representation" idea from my thesis to characterize Baire class alpha functions.

Jouko Väänänen: Delta(LQ1) is not finitely generated.
In this talk I sketch a proof that the so called Delta-extension of the quantifier "there exists uncountably many" cannot be generated by finitely many Lindstrom quantifiers, assuming CH. The proof involves the construction of two very similar but non-isomorphic models by forcing. An absoluteness argument is then used to eliminate the forcing. This is joint work with Saharon Shelah.