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arXiv · 2308.08293

Marginalia to a Theorem of Asper\'o and Schindler

Obrad Kasum·Boban Veličković
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Abstract

We give a game-theoretic characterization of when a model of an infinitary propositional formula can be added by a proper, semiproper, and stationary-set-preserving poset. In the latter case, we also give a general sufficient condition for the existence of such a poset. We use this condition to give a somewhat different proof of the theorem of Asper\'o and Schindler, which states that $\mathsf{MM}^{++}$ implies Woodin's axiom $(*)$.

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Obrad Kasum, Boban Veličković. 2023-08-16. Marginalia to a Theorem of Asper\'o and Schindler. https://arxiv.org/abs/2308.08293

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