The first-order definability of generic large cardinals

2021/06/27 by Sakaé Fuchino, Hiroshi Sakai, Fuchino, Sakaé +1 · 1 citation
Computer Science · Mathematics · #03E35 #03E50 #03E55 #03E65 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2106.14129

openalex publication_date 2021/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the notions of generic and Laver-generic supercompactness are first-order definable in the language of ZFC. This also holds for generic and Laver-generic (almost) hugeness as well as for generic versions of other large cardinals.

Cited by

• Extendible cardinals, and Laver-generic large cardinal axioms for extendibility

Related

• Generically supercompact cardinals by forcing with chain conditions
• Definable tree property for uncountable regular cardinals
• Incompatibility of generic hugeness principles
• All large-cardinal axioms not known to be inconsistent with ZFC are justified
• The large cardinals between supercompact and almost-huge