Randall Holmes: Consistency of New Foundations

Wednesday, December 9 from 3 to 4pm
Room: MP 207
Speaker: Randall Holmes (BSU)
Title: Consistency of New Foundations

Abstract: This will be the first of three or four talks which will give an account of my consistency proof for Quine’s system of set theory New Foundations (proposed by W. v.O. Quine in 1937). The first talk will cover preliminaries about the typed theory of sets (an unproblematic variant of the usual set theory), the modification of the definition of the typed theory of sets to give New Foundations, and the relevant known results about the model theory of NF and the relative consistency of related systems. The construction is via a Fraenkel-Mostowski construction of a model of ZFA (the usual set theory with atoms) without Choice, so the next point will be a discussion of this kind of construction, with an example relevant to the eventual main construction. All work done in the talk will actually be done in the usual set theory or variants (give or take the existence of atoms or the assumption of the axiom of choice).

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