Kurt Gödel Research Center

2015 seminar talk: Fragments of Kripke-Platek Set Theory

Talk held by Wei Li (KGRC) at the KGRC seminar on 2015-04-16.

Abstract

Fragments of the Kripke–Platek set theory deal with structures of set theory without full foundation. This is a joint project with Sy Friedman and Tin Lok Wong from the Kurt Gödel Research Center. One motivation of this project is the connection between nonstandard arithmetic and $\alpha$-recursion theory. $\alpha$-recursion theory has its generalized arguments in $L_\alpha$'s, where $\alpha$ is a standard ordinal. And in nonstandard arithmetic, we work in models without full induction. Induction is the dual of foundation. In their developments, techniques and results have many overlaps. Yet, reasons for this phenomenon are yet to be found. In this project, our research is done in nonstandard models of set theory. These models are "between" those in nonstandard arithmetic and those in $\alpha$-recursion theory. It is one attempt to search for the reason for the mysterious connections between these two areas.