$\mu$-Clubs OF $P_\kappa (\lambda)$ : Paradise on earth
Pierre Matet

TL;DR
This paper investigates the isomorphism of $$-club filters on certain power sets of cardinals, demonstrating new cases of such isomorphisms in ZFC beyond previous assumptions.
Contribution
It extends the understanding of $$-club filter isomorphisms to many new triples of cardinals within ZFC, surpassing prior results limited to $V=L$.
Findings
Many triples $(, , )$ have isomorphic $$-club filters in ZFC.
The isomorphism occurs even when $u(, ) > $, broadening previous conditions.
The results hold without assuming $V=L$, unlike earlier work.
Abstract
If , and , and are three infinite cardinals with , then, as shown in \cite{Heaven}, the -club filters on and are isomorphic if and only if . Now in , equals (the least size of a cofinal subset in ) equals if , and otherwise. We show that, in ZFC, there are many triples for which ( and) the -club filters on and are isomorphic.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Advanced Algebra and Logic
