Generalizations of Martin's Axiom, weak square, weak Chang's Conjecture, and a forcing axiom failure
| Autor: | Aspero, David, Tananimit, Nutt |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove that the forcing axiom $MA^{1.5}_{\aleph_2}(\mbox{stratified})$ implies $\Box_{\omega_1, \omega_1}$. Using this implication, we show that the forcing axiom $MM_{\aleph_2}(\aleph_2\mbox{-c.c.})$ is inconsistent. We also derive weak Chang's Conjecture from $MA^{1.5}_{\aleph_2}(\mbox{stratified})$ and use this second implication to give another proof of the inconsistency of $MM_{\aleph_2}(\aleph_2\mbox{-c.c.})$. Comment: 30 pages |
| Databáze: | arXiv |
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