A Forcing Axiom Deciding the Generalized Souslin Hypothesis

Chris Lambie-Hanson; Assaf Rinot

doi:https://doi.org/10.4153/CJM-2017-058-2

A Forcing Axiom Deciding the Generalized Souslin Hypothesis

Chris Lambie-Hanson, Assaf Rinot

Department of Mathematics

Bar-Ilan University

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

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

Keywords

SDFA
Souslin tree
diamond
forcing axiom
sharply dense set
square

All Science Journal Classification (ASJC) codes

General Mathematics

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https://doi.org/10.4153/CJM-2017-058-2

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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 G{\"o}del's constructible universe, then 2 λ = λ + entails the existence of a λ + -complete λ ++ -Souslin tree.",

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AB - 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.

KW - SDFA

KW - Souslin tree

KW - diamond

KW - forcing axiom

KW - sharply dense set

KW - square

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JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

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A Forcing Axiom Deciding the Generalized Souslin Hypothesis

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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