Notre Dame Journal of Formal Logic

Closed Maximality Principles and Generalized Baire Spaces

Philipp Lücke

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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.

Article information

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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Mathematical Reviews number (MathSciNet)

Primary: 03E57: Generic absoluteness and forcing axioms [See also 03E50]
Secondary: 03E35: Consistency and independence results 03E47: Other notions of set-theoretic definability

forcing axioms maximality principles generalized Baire spaces $\Sigma_{1}$-definability


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.

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