Consistency of Quine's New Foundations using nominal techniques

A Note on Eventually Complete Models of TypeTheory and Quine ' s New

We deene a property of models of simple type theory, viz. that of being eventually complete, and show that the existence of such models is equivalent to the consistency of Quine's New Foundations. Furthermore we show that the usual standard models are not eventually complete, although for models with an innnite domain of individuals, we lack examples of sentences witnessing this.

Zoolog Y: Weiss and Rossetti

1 Quine, W. V., "New Foundations for Mathematical Logic," American Mathematical Monthly, 44, 70-80 (1937). 2 Curry, H. B., review of same, Zentr. Mathematik, 16, 193 (1937). 3 Rosser, Barkley, "On the Consistency of Quine's 'New Foundations for Mathematical Logic,' "J. Symbolic Logic, 4, 15-24 (1939); Rosser, Barkley, and Wang, Hao, "Non-Standard Models for Formal Logics," Ibid., 15, 113-129 (1...

A Note on Eventually Complete Models of Type Theory and Quine's New Foundations

The Axiom of Choice in Quine's New Foundations for Mathematical Logic.

Equivariant ZFA and the foundations of nominal techniques

We give an accessible presentation to the foundations of nominal techniques, lying between Zermelo-Fraenkel set theory and Fraenkel-Mostowski set theory, and which has several nice properties including being consistent with the Axiom of Choice. We give two presentations of equivariance, accompanied by detailed yet user-friendly discussions of its theoretical significance and practical application.