Consistency of strictly impredicative NF and a little more …
Sergei Tupailo · Journal of Symbolic Logic · 2010
Abstract An instance of Stratified Comprehension is calledstrictly impredicativeiff, under minimal stratification, the type ofxis 0. Using the technology of forcing, we prove that the fragment ofNFbased 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 arenotstrictly impredicative. For example, it verifies existence of Frege natural numbers. Apparently, this is a new subsystem ofNFshown to be consistent. The consistency question for the whole theoryNFremains open (since 1937).