Sets Theory and Antinomies: a Note
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- Set Theory, Improper Subsets, Antinomies, Grellings Paradox, Liar Paradox
- Antonio Luigi Paolilli
- In Frege Set Theory the axiom of unlimited abstraction causes various antinomies, revealing a lack of congruence of the same theory. Some solutions to this problem have been advanced by Russell, Whitehead and Zermelo. In this note it is shown a way to abolish the assumption that a set can be a subset of itself, so allowing us to solve various antinomies in a simpler way.
Full text: IJISM_666_FINAL.pdf