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May 2019 Closed Maximality Principles and Generalized Baire Spaces
Philipp Lücke
Notre Dame J. Formal Logic 60(2): 253-282 (May 2019). DOI: 10.1215/00294527-2019-0004

Abstract

Given an uncountable regular cardinal κ, we study the structural properties of the class of all sets of functions from κ to κ that are definable over the structure H(κ+), by a Σ1-formula with parameters. It is well known that many important statements about these classes are not decided by the axioms of ZFC together with large cardinal axioms. In this paper, we present other canonical extensions of ZFC 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.

Citation

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Philipp Lücke. "Closed Maximality Principles and Generalized Baire Spaces." Notre Dame J. Formal Logic 60 (2) 253 - 282, May 2019. https://doi.org/10.1215/00294527-2019-0004

Information

Received: 17 July 2016; Accepted: 17 February 2017; Published: May 2019
First available in Project Euclid: 8 May 2019

zbMATH: 07096538
MathSciNet: MR3952233
Digital Object Identifier: 10.1215/00294527-2019-0004

Subjects:
Primary: 03E57
Secondary: 03E35, 03E47

Rights: Copyright © 2019 University of Notre Dame

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Vol.60 • No. 2 • May 2019
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