TL;DR
This paper demonstrates that an extendible cardinal can be preserved through a set forcing that is not small, answering a question posed by Usuba.
Contribution
It provides a novel set forcing method that preserves extendible cardinals without requiring the forcing to be small, advancing understanding in large cardinal preservation.
Findings
Extendible cardinals can be preserved by non-small set forcing.
A specific forcing method was constructed to achieve this preservation.
The result answers an open question by Usuba.
Abstract
Answering a question of Usuba, we show that an extendible cardinal can be preserved by a set forcing that is not a small forcing.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Advanced Banach Space Theory