Many forcing axioms for all regular uncountable cardinals

Noam Greenberg*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 having a strong forcing axiom of higher order than usual. Instead of “every suitable forcing notion of size λ has a sufficiently generic filter” we shall say “for every suitable method of producing notions of forcing based on a given stationary set, there is such a suitable stationary set S and sufficiently generic filters for the notion of forcing attached to S”. Such notions of forcing are important for Abelian group theory, but this application is delayed for a sequel.

Original languageEnglish
Pages (from-to)127-170
Number of pages44
JournalIsrael Journal of Mathematics
Volume261
Issue number1
DOIs
StatePublished - Jun 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2023.

Fingerprint

Dive into the research topics of 'Many forcing axioms for all regular uncountable cardinals'. Together they form a unique fingerprint.

Cite this