Another method to add a closed unbounded set of former regulars
Moti Gitik, Sittinon Jirattikansakul
TL;DR
This paper introduces a new method for adding a closed unbounded set of former regulars to an inaccessible cardinal using a variation of Radin forcing, without altering cofinalities outside the set.
Contribution
It presents a novel Radin forcing variation that operates without requiring a top measurable cardinal, expanding the tools for set-theoretic constructions.
Findings
Successfully adds a club of former regulars to an inaccessible cardinal.
Maintains cofinalities outside the added set.
Operates without a top measurable cardinal.
Abstract
A club consisting of former regulars is added to an inaccessible cardinal, without changing cofinalities outside it. The initial assumption is optimal. A variation of the Radin forcing without a top measurable cardinal is introduced for this.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Rings, Modules, and Algebras