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Results tagged with axioms
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user 8991
38
votes
Accepted
How undecidable is the spectral gap?
The connection to things like axiomitizations of math is then completely standard---any correct and consistent system of axioms cannot prove "$H^{\Lambda(L)}(n)$ is not gapped" for all $n$ for which this …
- 7,145
6
votes
What are the advantages of the more abstract approaches to nonstandard analysis?
For most purposes, I think the premise is wrong: in many situations ultraproducts simply are the preferable approach, so I'll try to discuss some of the purposes which are exceptions. @cody has alrea …
- 7,145
76
votes
Accepted
How should a "working mathematician" think about sets? (ZFC, category theory, urelements)
Set theory provides a foundation for mathematics in roughly the same way that Turing machines provide a foundation for computer science. A computer program written in Java or assembly language isn't …
- 7,145