# Incompatible category forcing axioms

David Aspero, Matteo Viale

Research output: Contribution to journalArticle

## 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. 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.
Original language English 45 Journal of Mathematical Logic (jml) Submitted - 2018