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arXiv · 1805.08732

Incompatible category forcing axioms

David Aspero·Matteo Viale
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Abstract

Given a cardinal $\lambda$, category forcing axioms for $\lambda$-suitable classes $\Gamma$ are strong forcing axioms which completely decide the theory of the Chang model $\mathcal C_\lambda$, modulo generic extensions via forcing notions from $\Gamma$. $\mathsf{MM}^{+++}$ was the first category forcing axiom to be isolated (by the second author). In this paper we present, without proofs, a general theory of category forcings, and prove the existence of $\aleph_1$-many pairwise incompatible category forcing axioms for $\omega_1$-suitable classes.

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David Aspero, Matteo Viale. 2018-05-22. Incompatible category forcing axioms. https://arxiv.org/abs/1805.08732

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