Woodin for strong compactness cardinals

TL;DR

This paper introduces Woodin for strong compactness cardinals, a new concept extending strong compactness, and proves an analogue of Magidor's identity crisis theorem for the first such cardinal.

Contribution

It defines Woodin for strong compactness cardinals and establishes a key theorem analogous to Magidor's identity crisis theorem.

Findings

Introduction of Woodin for strong compactness cardinals

Proved an analogue of Magidor's identity crisis theorem

Extended understanding of strong compactness concepts

Abstract

We give the definition of Woodin for strong compactness cardinals, the Woodinised version of strong compactness, and we prove an analogue of Magidor's identity crisis theorem for the first strongly compact cardinal.