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 | ||||||
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| Keywords: | Large cardinals, set theory, foundations of mathematics | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics |
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| 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 |
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| Date: | 2018 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/15909 |
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Large Cardinals and the Iterative Conception of Set. (deposited 06 May 2018 15:33)
- Large Cardinals and the Iterative Conception of Set. (deposited 15 Apr 2019 18:11) [Currently Displayed]
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