AD or AC?

the diagram

A fancy diagram of the consequences of real choice. This was part of a project during my masters' studies at the ILLC concerning the relationship between choice and determinacy. I gave a talk on that project at the Logic Colloquium 2005 in Athens. Later on it may be modified to include RGB colouring according to compatibility with determinacy. Red will mark an incompatible with AD fragment, green a fragment that is also fragment of AD and blue will mark consistency and/or independence from AD. Any comments will be very welcome. References will be given after request.

second order arithmetic talk

GLLC 14½ talk: Topological regularities in second order arithmetic

I am very happy that I was invited at the “Games in Logic, Language and Computation 14½" meeting at the ILLC in Amsterdam (where I finished my masters) to give this talk. The talk is based on work by Peter Koepke and Michael Möllerfeld. It shows that ZFC is equiconsistent with full second order arithmetic (SOA) plus all sets of reals are Lebesgue measurable, have the Baire property and the perfect set property. I helped finish off the forcing side (which admittedly is a bit disappointingly easy). These are the slides.

logic colloquium 2007

LC2007 talk: Equiconsistency of choiceless higher Chang conjectures with one Erdos cardinal

These are the slides from my talk at the Logic Colloquium 2007 in Wroclaw, Poland. They describe an equiconsistency proof, i.e., [ZFC + κ is λ-Erdos] is equiconsistent with [ZF+ (λ⁺,λ)—»(λ,ν)] for every infinite ν< λ and λ regular. If you are bothered by the quantifiers outside of the equiconsistency statements (i.e., "for every λ regular cardinal" and "for every infinite ν below λ"), just call this "transitive model equiconsistent". From left to right it's a simple symmetric collapse and from right to left it's looking at the Dodd-Jensen core model. If you like the pictures and want to use them, just drop me an email!

BIGS poster session

BIGS poster 2007

This is the poster I prepared for the PhD poster day of BIGS (Bonn International Graduate School). This is an annual event (every June) in which PhD students of Mathematics are given a template and are asked to use it to create posters presenting their research to the rest of the institute. Coffee and cake are offered and for three hours members of the Mathematical institute go around talking about these posters. My poster is intended to be readable by the average member of a Mathematical institute, gives a short answer to the question "why set theory" and "why large cardinals without choice" and a brief exposition of my research at the time.