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Results tagged with foundations
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user 13530
Mathematical logic, Set theory, Peano arithmetic, Model theory, Proof theory, Recursion theory, Computability theory, Univalent foundations, Reverse mathematics, Frege foundation of arithmetic, Goedel's incompleteness and Mathematics, Structural set theory, Category theory, Type theory.
5
votes
Where is the end of universe?
Have a look at Church’s (first) Set Theory with a Universal Set, which is equiconsistent with ZFGC, though Church didn’t publish a full proof, and I think he abandoned the proof in his archives at Pri …
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3
votes
Set theory and alternative foundations
To follow up further on Joel David Hamkins's answer on geometry, Frege’s last work (two despairing decades after Russell’s Paradox demolished his Grundgesetze der Arithmetik) was a brief unpublished p …
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3
votes
Applications of ZFA-Set Theory
Arnold Oberschelp used urelements in his relative consistency proof of a set theory with a universal set and the singleton function as a set. I followed his example in my variant of Alonzo Church’s “ …
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2
votes
Anti-foundational set theory with a universal set
Check out the theory at the end of Vicious Circles by Barwise & Moss, which has the Universal Set U, though the “collection of all sets distinct from U will not be a class.” (p. 308). I crafted some …
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