2022/06/19 by Vincenzo Dimonte, Dimonte, Vincenzo
Arts and Humanities · Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Philosophy and History of Science
paper · pdf · doi:10.48550/arxiv.2206.09442
openalex publication_date 2022/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Kunen's proof of the non-existence of Reinhardt cardinals opened up the research on very large cardinals, i.e., hypotheses at the limit of inconsistency. One of these large cardinals, I0, proved to have descriptive-set-theoretical characteristics, similar to those implied by the Axiom of Determinacy: if λ witnesses I0, then there is a topology for Vλ+1 that is completely metrizable and with weight λ (i.e., it is a λ-Polish space), and it turns out that all the subsets of Vλ+1 in L(Vλ+1) have the λ-Perfect Set Property in such topology. In this paper, we find another generalized Polish space of singular weight κ of cofinality ω such that all its subsets have the κ-Perfect Set Property, and in doing this, we are lowering the consistency strength of such property from I0 to κ θ-supercompact, with θ>κ inaccessible.