Incompatible bounded category forcing axioms

Asperó, David and Viale, Matteo (2022) Incompatible bounded category forcing axioms. Journal of Mathematical Logic, 22 (2). ISSN 0219-0613

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Abstract

We introduce bounded category forcing axioms for well-behaved classes Γ. These are strong forms of bounded forcing axioms which completely decide the theory of some initial segment of the universe Hλ+Γ modulo forcing in Γ, for some cardinal λΓ naturally associated to Γ. These axioms naturally extend projective absoluteness for arbitrary set-forcing — in this situation λΓ=ω — to classes Γ with λΓ>ω. Unlike projective absoluteness, these higher bounded category forcing axioms do not follow from large cardinal axioms but can be forced under mild large cardinal assumptions on V. We also show the existence of many classes Γ with λΓ=ω1 giving rise to pairwise incompatible theories for Hω2.

Item Type:	Article
Uncontrolled Keywords:	bounded category forcing axioms,category forcing,forcing axioms,large cardinals,projective resurrection,logic ,/dk/atira/pure/subjectarea/asjc/2600/2609
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	17 Oct 2022 10:32
Last Modified:	07 Nov 2024 12:40
URI:	https://ueaeprints.uea.ac.uk/id/eprint/89117
DOI:	10.48550/arXiv.2101.03132

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