First-order Goedel logics
Logic
2015-04-21 v1
Abstract
First-order Goedel logics are a family of infinite-valued logics where the sets of truth values V are closed subsets of [0, 1] containing both 0 and 1. Different such sets V in general determine different Goedel logics G_V (sets of those formulas which evaluate to 1 in every interpretation into V). It is shown that G_V is axiomatizable iff V is finite, V is uncountable with 0 isolated in V, or every neighborhood of 0 in V is uncountable. Complete axiomatizations for each of these cases are given. The r.e. prenex, negation-free, and existential fragments of all first-order Goedel logics are also characterized.
Keywords
Cite
@article{arxiv.math/0601147,
title = {First-order Goedel logics},
author = {Matthias Baaz and Norbert Preining and Richard Zach},
journal= {arXiv preprint arXiv:math/0601147},
year = {2015}
}
Comments
37 pages