The Tree Property

Given an uncountable tree with countable levels, is there always an uncountable branch? To formulate this question properly takes some work, which we will do, and we will then see that the answer is quite subtle. Along the way, we will see singular, regular, inaccessible, measurable, and supercompact cardinals, and have a glimpse of how forcing works.

Authors

Publication Details

Journal
Notices of the American Mathematical Society
Published
2025-11-01
DOI
https://doi.org/10.1090/noti3268
Primary Topic
Advanced Topology and Set Theory
Type
article
Field-Weighted Citation Impact
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article

The Tree Property

Dima Sinapova
Notices of the American Mathematical Society
Advanced Topology and Set Theory
article

The Tree Property

Dima Sinapova
article en

Abstract

Given an uncountable tree with countable levels, is there always an uncountable branch? To formulate this question properly takes some work, which we will do, and we will then see that the answer is quite subtle. Along the way, we will see singular, regular, inaccessible, measurable, and supercompact cardinals, and have a glimpse of how forcing works.

Notices of the American Mathematical SocietyVol. 72(10)
Openalex Percentile: Top 59%
Advanced Topology and Set Theory
DOISourceOpenAlex
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The Tree Property — Dima Sinapova · Notices of the American Mathematical Society (2025) | TGRS Research Map | TGRS