Polish space partition principles and the Halpern-Läuchli theorem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00605668" target="_blank" >RIV/67985840:_____/24:00605668 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/jsl.2024.4" target="_blank" >https://doi.org/10.1017/jsl.2024.4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/jsl.2024.4" target="_blank" >10.1017/jsl.2024.4</a>

Result language
angličtina
Original language name
Polish space partition principles and the Halpern-Läuchli theorem
Original language description
The Halpern-Läuchli theorem, a combinatorial result about trees, admits an elegant proof due to Harrington using ideas from forcing. In an attempt to distill the combinatorial essence of this proof, we isolate various partition principles about products of perfect Polish spaces. These principles yield straightforward proofs of the Halpern-Läuchli theorem, and the same forcing from Harrington s proof can force their consistency. We also show that these principles are not ZFC theorems by showing that they put lower bounds on the size of the continuum.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA23-04683S" target="_blank" >GA23-04683S: Compactness in set theory, with applications to algebra and graph theory</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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