Characterization of the Axiomatizable Prenex Fragments of First-Order Goedel Logics
Matthias Baaz, Norbert Preining, Richard Zach
TL;DR
This paper classifies the axiomatizability of prenex fragments in first-order infinite-valued Goedel logics, showing that some are axiomatizable while others are not, based on the subset of [0,1].
Contribution
It provides a complete classification of which prenex fragments of first-order Goedel logics are axiomatizable, depending on the nature of the subset of [0,1].
Findings
Prenex Goedel logics with finite or uncountable subsets of [0,1] are axiomatizable.
Countably infinite prenex Goedel logics are not axiomatizable.
The classification depends on the cardinality of the subset of [0,1].
Abstract
The prenex fragments of first-order infinite-valued Goedel logics are classified. It is shown that the prenex Goedel logics characterized by finite and by uncountable subsets of [0, 1] are axiomatizable, and that the prenex fragments of all countably infinite Goedel logics are not axiomatizable.
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Taxonomy
TopicsAdvanced Algebra and Logic · Logic, Reasoning, and Knowledge