English

Generalizations of Martin's Axiom, weak square, weak Chang's Conjecture, and a forcing axiom failure

Logic 2022-12-15 v1

Abstract

We prove that the forcing axiom MA21.5(\mboxstratified)MA^{1.5}_{\aleph_2}(\mbox{stratified}) implies ω1,ω1\Box_{\omega_1, \omega_1}. Using this implication, we show that the forcing axiom MM2(2\mboxc.c.)MM_{\aleph_2}(\aleph_2\mbox{-c.c.}) is inconsistent. We also derive weak Chang's Conjecture from MA21.5(\mboxstratified)MA^{1.5}_{\aleph_2}(\mbox{stratified}) and use this second implication to give another proof of the inconsistency of MM2(2\mboxc.c.)MM_{\aleph_2}(\aleph_2\mbox{-c.c.}).

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Cite

@article{arxiv.2212.07324,
  title  = {Generalizations of Martin's Axiom, weak square, weak Chang's Conjecture, and a forcing axiom failure},
  author = {David Aspero and Nutt Tananimit},
  journal= {arXiv preprint arXiv:2212.07324},
  year   = {2022}
}

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30 pages