Łoś's theorem and the axiom of choice

In set theory without the Axiom of Choice (AC), we investigate the problem of the placement of Łoś's Theorem (LT) in the hierarchy of weak choice principles, and answer several open questions from the book Consequences of the Axiom of Choice by Howard and Rubin, as well as an open question by B...

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Bibliographic Details
Published in:Mathematical logic quarterly 2019-10, Vol.65 (3), p.280-292
Main Author: Tachtsis, Eleftherios
Format: Article
Language:English
Subjects:
Questions
Set theory
Theorems
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Summary:In set theory without the Axiom of Choice (AC), we investigate the problem of the placement of Łoś's Theorem (LT) in the hierarchy of weak choice principles, and answer several open questions from the book Consequences of the Axiom of Choice by Howard and Rubin, as well as an open question by Brunner. We prove a number of results summarised in § 3.
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.201700074