2010 seminar talk: Non-proper Elementary Embeddings Beyond L(Vλ+1)
Talk held by Vincenzo Dimonte (KGRC) at the KGRC seminar on 2010-03-25.
In a recent work Woodin has defined new axioms stronger than I0 (the existence of an elementary embedding j from L(Vλ+1) to itself), that involve elementary embeddings between slighter large models. While the correspondence between I0 and Determinacy carries on without further hypotheses, for these new axioms we need the embeddings to be proper. This initially seemed a common property, but during the seminar there will be presented two essentially different cases of non-proper elementary embeddings. These results fill a gap in a Theorem by Woodin and legitimate the definition of properness.