Many forcing axioms for all regular uncountable cardinals

Noam Greenberg; Saharon Shelah

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arXiv · 2107.05755

Many forcing axioms for all regular uncountable cardinals

Noam Greenberg·Saharon Shelah

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Abstract

A central theme in set theory is to find universes with extreme, well-understood behaviour. The case we are interested in is assuming GCH and has a strong forcing axiom of higher order than usual. Instead of "for every suitable forcing notion for~$\lambda$" we shall say "for every such family of forcing notions, depending on stationary $S\subseteq \lambda$, for some such stationary set we have\dots". Such notions of forcing are important for Abelian group theory, but this application is delayed for a sequel.

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BibTeX RIS

Noam Greenberg, Saharon Shelah. 2021-07-12. Many forcing axioms for all regular uncountable cardinals. https://arxiv.org/abs/2107.05755

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