NF in the Bay Area

Thomas Forster (University of Cambridge)
A Discussion of Some Open Problem in NF and Related Systems

See (current draught).

Randall Holmes (Boise State University)
Symmetry, Comprehension and Indiscernibility of Urelements in NFU

Holmes will discuss symmetry as a criterion for comprehension motivating NFU, with related questions about term models of NFU and TST, and further discuss the demonstration that the urelements in NFU are discernible in the "usual models of NFU", in spite of the fact that symmetry arguments show that they are indiscernible with respect to stratified formulas, because it turns out that the membership relation of the nonstandard model of the usual set theory underlying a "usual model" of NFU is definable in terms of the membership relation of the model of NFU, so urelements can be distinguished using properties of their original extensions.

Sergei Tupailo (Stanford University)
Consistency of Strictly Impredicative NF

An instance of Stratified Comprehension

x1…∀xnyx (xy ↔ φ(x,x1,…,xn))

is called strictly impredicative iff, under minimal stratification, the type of x is 0. Using the technology of forcing, we prove that the fragment of NF based on strictly impredicative Stratified Comprehension is consistent. A crucial part in this proof, namely showing genericity of a certain symmetric filter, is due to Robert Solovay.

As a bonus, our interpretation also satisfies some instances of Stratified Comprehension which are not strictly impredicative. For example, it verifies existence of Frege natural numbers.