A Forcing Axiom Deciding the Generalized Souslin Hypothesis

Chris Lambie-Hanson; Assaf Rinot

doi:10.4153/CJM-2017-058-2

A Forcing Axiom Deciding the Generalized Souslin Hypothesis

Chris Lambie-Hanson, Assaf Rinot

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal λ, if λ ⁺⁺ is not a Mahlo cardinal in Gödel's constructible universe, then 2 ^λ = λ ⁺ entails the existence of a λ ⁺ -complete λ ⁺⁺ -Souslin tree.

Original language	English
Pages (from-to)	437-470
Number of pages	34
Journal	Canadian Journal of Mathematics
Volume	71
Issue number	2
DOIs	https://doi.org/10.4153/CJM-2017-058-2
State	Published - 1 Apr 2019

Bibliographical note

Publisher Copyright:
© 2018 Canadian Mathematical Society.

Funding

This research was partially supported by the Israel Science Foundation (grant #1630/14).

Funders	Funder number
Israel Science Foundation	1630/14

Keywords

SDFA
Souslin tree
diamond
forcing axiom
sharply dense set
square

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10.4153/CJM-2017-058-2

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A Forcing Axiom Deciding the Generalized Souslin Hypothesis

Abstract

Bibliographical note

Funding

Keywords

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