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

2022/12/14 by David Asperó, Aspero, David, Nutt Tananimit +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2212.07324

openalex publication_date 2022/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the forcing axiom MA^1.5_ℵ2(stratified) implies \Box_{ω1, ω1}. Using this implication, we show that the forcing axiom MM_ℵ2(ℵ₂-c.c.) is inconsistent. We also derive weak Chang's Conjecture from MA^1.5_ℵ2(stratified) and use this second implication to give another proof of the inconsistency of MM_ℵ2(ℵ₂-c.c.).

Related

• A Generalization of Martin's Axiom
• An Inconsistent Forcing Axiom at ω₂
• Martin's maximum revisited
• Distinguishing Martin's axiom from its restrictions
• Useful axioms