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Large Cardinals and the Iterative Conception of Set

Barton, Neil (2018) Large Cardinals and the Iterative Conception of Set. [Preprint]

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Abstract

The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles for the iterative conception, and assert that the length of the iterative stages is as long as possible. In this paper, we argue that whether or not large cardinal principles count as maximality principles depends on prior commitments concerning the richness of the subset forming operation. In particular we argue that there is a conception of maximality through absoluteness, that when given certain technical formulations, supports the idea that large cardinals are consistent, but false. On this picture, large cardinals are instead true in inner models and serve to restrict the subsets formed at successor stages.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Barton, Neilbartonna@gmail.com0000-0002-3637-1730
Keywords: Large cardinals, set theory, foundations of mathematics
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics
Depositing User: Dr. Neil Barton
Date Deposited: 15 Apr 2019 18:11
Last Modified: 15 Apr 2019 18:11
Item ID: 15909
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics
Date: 2018
URI: http://philsci-archive.pitt.edu/id/eprint/15909

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