Incompatible bounded category forcing axioms

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

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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
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Logic
Depositing User: LivePure Connector
Date Deposited: 17 Oct 2022 10:32
Last Modified: 22 Oct 2022 04:24
DOI: 10.48550/arXiv.2101.03132


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