The hyperuniverse program

Bulletin of Symbolic Logic 19 (1):77-96 (2013)
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Abstract

The Hyperuniverse Program is a new approach to set-theoretic truth which is based on justifiable principles and leads to the resolution of many questions independent from ZFC. The purpose of this paper is to present this program, to illustrate its mathematical content and implications, and to discuss its philosophical assumptions.

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Citations of this work

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Forcing and the Universe of Sets: Must We Lose Insight?Neil Barton - 2020 - Journal of Philosophical Logic 49 (4):575-612.
Maximality Principles in Set Theory.Luca Incurvati - 2017 - Philosophia Mathematica 25 (2):159-193.
Varieties of Class-Theoretic Potentialism.Neil Barton & Kameryn J. Williams - 2024 - Review of Symbolic Logic 17 (1):272-304.

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References found in this work

The set-theoretic multiverse.Joel David Hamkins - 2012 - Review of Symbolic Logic 5 (3):416-449.
The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Philosophy of mathematics, selected readings.Paul Benacerraf & Hilary Putnam - 1966 - Revue Philosophique de la France Et de l'Etranger 156:501-502.
Believing the axioms. II.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (3):736-764.
On reflection principles.Peter Koellner - 2009 - Annals of Pure and Applied Logic 157 (2-3):206-219.

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