Every set of first-order formulas is equivalent to an independent set
Ioannis Souldatos (for the translation), I. Reznikoff (for the, original French)
TL;DR
This paper proves that any set of first-order formulas can be transformed into an equivalent independent set, regardless of the size of the symbol set.
Contribution
It establishes a general equivalence result for first-order formulas, showing they can always be represented as independent sets.
Findings
Any set of first-order formulas is equivalent to an independent set
The equivalence holds regardless of the cardinality of the symbol set
Provides a foundational result in logical formula manipulation
Abstract
A set of first-order formulas, whatever the cardinality of the set of symbols, is equivalent to an independent set.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rough Sets and Fuzzy Logic · semigroups and automata theory