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Results tagged with new-foundations
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user 13530
New Foundations is the axiomatic set theory in Quine's 1937 article "New Foundations for Mathematical Logic"; it simplifies the theory of types of Principia Mathematica.
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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5
votes
How much of ZFC does Quine's New Foundations prove?
While I second (with highly biased motivation) the recommendation of Forster’s book, for questions like this an easier starting point than Forster’s book or Holmes’ articles might be Holmes’ book Elem …
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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last work (two despairing decades after Russell’s Paradox demolished his Grundgesetze der Arithmetik) was a brief unpublished p …
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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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1
vote
Consistency of the concept of the collection of all collection
Church’s “Set Theory with a Universal Set” (see, e.g., Thomas Forster’s article) has a set of all sets, and Church provides a model (actually an interpretation in ZFGC) for it. He never published the …
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