Variations on a Visserian Theme
Logic
2017-02-24 v1
Abstract
A first order theory T is said to be "tight" if for any two deductively closed extensions U and V of T (both of which are formulated in the language of T), U and V are bi-interpretable iff U = V. By a theorem of Visser, PA (Peano Arithmetic) is tight. Here we show that Z_2 (second order arithmetic), ZF (Zermelo-Fraenkel set theory), and KM (Kelley-Morse theory of classes) are also tight theories.
Cite
@article{arxiv.1702.07093,
title = {Variations on a Visserian Theme},
author = {Ali Enayat},
journal= {arXiv preprint arXiv:1702.07093},
year = {2017}
}
Comments
16 pages