Philosophia Mathematica 25 (2):159-193 (2017)

Authors
Luca Incurvati
University of Amsterdam
Abstract
In set theory, a maximality principle is a principle that asserts some maximality property of the universe of sets or some part thereof. Set theorists have formulated a variety of maximality principles in order to settle statements left undecided by current standard set theory. In addition, philosophers of mathematics have explored maximality principles whilst attempting to prove categoricity theorems for set theory or providing criteria for selecting foundational theories. This article reviews recent work concerned with the formulation, investigation and justification of maximality principles.
Keywords Maximality principles  Set theory  Iterative conception  Reflection principles  Inner model hypothesis  Forcing axioms  Restrictiveness
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DOI 10.1093/philmat/nkw011
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References found in this work BETA

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
The Potential Hierarchy of Sets.Øystein Linnebo - 2013 - Review of Symbolic Logic 6 (2):205-228.
The Set-Theoretic Multiverse.Joel David Hamkins - 2012 - Review of Symbolic Logic 5 (3):416-449.

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From Metasemantics to Analyticity.Zeynep Soysal - forthcoming - Philosophy and Phenomenological Research.

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