Woodin cardinals and forcing
Stamatis Dimopoulos
TL;DR
This paper reviews known results on Woodin cardinals, provides a template for their preservation under forcing, and establishes an indestructibility result via Easton iterations.
Contribution
It introduces a general template for preserving Woodin cardinals through forcing and demonstrates their indestructibility under specific Easton iterations.
Findings
Preservation of Woodin cardinals under certain forcing extensions
A template for maintaining Woodin cardinals during forcing
Indestructibility of Woodin cardinals under Easton iterations
Abstract
Despite being an established notion in the large cardinal hierarchy, results about Woodin cardinals are sparse in the literature. Here we gather known results about the preservation of Woodin cardinals under certain forcing extensions, as well as giving a template for preserving Woodin cardinals through forcing. Using this template, we form an indestructibility result under certain Easton iterations.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Mathematical and Theoretical Analysis