Philosophia Mathematica 25 (2):159-193 (2017)
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| 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.
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| 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
Foundations Without Foundationalism: A Case for Second-Order Logic.Stewart Shapiro - 1991 - Oxford University Press.
What is Cantor's Continuum Problem?Kurt Gödel - 1947 - In Solomon Feferman, John Dawson & Stephen Kleene (eds.), Journal of Symbolic Logic. Oxford University Press. pp. 176--187.
View all 78 references / Add more references
Citations of this work BETA
From Metasemantics to Analyticity.Zeynep Soysal - forthcoming - Philosophy and Phenomenological Research.
Maddy On The Multiverse.Claudio Ternullo - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Berlin: Springer Verlag. pp. 43-78.
Maximality Principles in the Hyperuniverse Programme.Sy-David Friedman & Claudio Ternullo - forthcoming - Foundations of Science:1-19.
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