Kurt Gödel Research Center

2019 seminar talk: L[Reg]

Talk held by Sy-David Friedman (KGRC) at the KGRC seminar on 2019-11-14.

Abstract

Gitik and I showed that L[Reg], like L[Card] and V, is a forcing extension of an iterate of a mouse. For L[Card] the mouse is the least one with a measurable limit of measurables (result of Philip Welch) and for V it's Mighty Mouse. For L[Reg] it's the least mouse with a measure concentrating on measurables, but the iterate may have to be truncated (for example if there are no regular limit cardinals). We use Magidor's iteration of Prikry forcings. An unexpected twist is that we need to use old-fashioned mice and not fine-structural mice for the proof.

Slides for this talk are available.