On wide Aronszajn trees in the presence of MA

Dzamonja, Mirna and Shelah, Saharon (2021) On wide Aronszajn trees in the presence of MA. Journal of Symbolic Logic, 86 (1). pp. 210-223. ISSN 0022-4812

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Abstract

A wide Aronszajn tree is a tree of size and height with no uncountable branches. We prove that under there is no wide Aronszajn tree which is universal under weak embeddings. This solves an open question of Mekler and Väänänen from 1994. We also prove that under, every wide Aronszajn tree weakly embeds in an Aronszajn tree, which combined with a result of Todorčević from 2007, gives that under every wide Aronszajn tree embeds into a Lipschitz tree or a coherent tree. We also prove that under there is no wide Aronszajn tree which weakly embeds all Aronszajn trees, improving the result in the first paragraph as well as a result of Todorčević from 2007 who proved that under there are no universal Aronszajn trees.

Item Type:	Article
Additional Information:	The accepted version not put in the journal form
Uncontrolled Keywords:	wide aronszajn tree,martin axiom,universality,mathematics(all) ,/dk/atira/pure/subjectarea/asjc/2600
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	04 Jun 2020 00:07
Last Modified:	17 Jul 2025 23:55
URI:	https://ueaeprints.uea.ac.uk/id/eprint/75460
DOI:	10.1017/jsl.2020.42

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