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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. One idea sometimes alluded to is that maximality considerations speak in favour of large cardinal axioms consistent with ZFC, since it appears to be `possible' (in some sense) to continue the hierarchy far enough to generate the relevant transfinite number. In this paper, we argue against this idea based on a priority of subset formation under the iterative conception. In particular, we argue that there are several conceptions of maximality that justify the consistency but falsity of large cardinal axioms. We argue that the arguments we provide are illuminating for the debate concerning the justification of new axioms in iteratively-founded set theory.

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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: 06 May 2018 15:33
Last Modified: 06 May 2018 15:33
Item ID: 14638
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics
Date: 2018
URI: https://philsci-archive.pitt.edu/id/eprint/14638

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