First-order Gödel logics

Annals of Pure and Applied Logic 147 (1):23-47 (2007)
  Copy   BIBTEX

Abstract

First-order Gödel logics are a family of finite- or 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 Gödel logics GV (sets of those formulas which evaluate to 1 in every interpretation into V). It is shown that GV 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 Gödel logics are also characterized.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2009-01-28

Downloads
68 (#217,390)

6 months
2 (#668,348)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Richard Zach
University of Calgary

References found in this work

A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Zum intuitionistischen aussagenkalkül.K. Gödel - 1932 - Anzeiger der Akademie der Wissenschaften in Wien 69:65--66.
Descriptive Set Theory.Richard Mansfield - 1981 - Journal of Symbolic Logic 46 (4):874-876.
Logic with truth values in a linearly ordered Heyting algebra.Alfred Horn - 1969 - Journal of Symbolic Logic 34 (3):395-408.

View all 17 references / Add more references