Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 60, Number 2 (2019), 253-282.
Closed Maximality Principles and Generalized Baire Spaces
Given an uncountable regular cardinal , we study the structural properties of the class of all sets of functions from to that are definable over the structure by a -formula with parameters. It is well known that many important statements about these classes are not decided by the axioms of together with large cardinal axioms. In this paper, we present other canonical extensions of that provide a strong structure theory for these classes. These axioms are variations of the Maximality Principle introduced by Stavi and Väänänen and later rediscovered by Hamkins.
Notre Dame J. Formal Logic, Volume 60, Number 2 (2019), 253-282.
Received: 17 July 2016
Accepted: 17 February 2017
First available in Project Euclid: 8 May 2019
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Lücke, Philipp. Closed Maximality Principles and Generalized Baire Spaces. Notre Dame J. Formal Logic 60 (2019), no. 2, 253--282. doi:10.1215/00294527-2019-0004. https://projecteuclid.org/euclid.ndjfl/1557281186