# Large Cardinals and the Iterative Conception of Set

@inproceedings{Barton2018LargeCA, title={Large Cardinals and the Iterative Conception of Set}, author={Neil Barton}, year={2018} }

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…

## One Citation

### Might All Infinities Be the Same Size?

- PhilosophyAustralasian Journal of Philosophy
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ABSTRACT Cantor proved that no set has a bijection between itself and its power set. This is widely taken to have shown that there infinitely many sizes of infinite sets. The argument depends on the…

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