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!