A definability theorem for first order logic
Logic
2016-09-07 v1
Abstract
For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order formula. Our presentation is entirely selfcontained, and only requires familiarity with the most elementary properties of model theory.
Cite
@article{arxiv.math/9706206,
title = {A definability theorem for first order logic},
author = {Carsten Butz and Ieke Moerdijk},
journal= {arXiv preprint arXiv:math/9706206},
year = {2016}
}