Die Vollständigkeit der Axiome des logischen Funktionenkalküls¶
Gödel, K. (1930). Die Vollständigkeit der Axiome des logischen Funktionenkalküls. Monatshefte für Mathematik und Physik, 349-360.
Cited by¶
2 citations across 2 artifacts.
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Primes¶
- Completeness
- A logical proof system is deductively complete with respect to a class of models when every formula valid in all models of that class admits a syntactic proof from the axioms (first-order classical logic is complete with respect to its model-theoretic semantics — Gödel's completeness theorem of 1929
This sourceEstablishes the completeness of first-order classical logic with respect to its model-theoretic semantics: every formula valid in all models of the axioms admits a finite syntactic proof.
- A logical proof system is deductively complete with respect to a class of models when every formula valid in all models of that class admits a syntactic proof from the axioms (first-order classical logic is complete with respect to its model-theoretic semantics — Gödel's completeness theorem of 1929
- Deductive Reasoning
- For classical first-order logic, the two are equivalent (completeness of first-order logic
This sourceWebSearch confirmed this is the source for the syntactic⇔semantic 'completeness of first-order logic' claim. Re-sourced from turing-1936, which proves Entscheidungsproblem undecidability, NOT first-order completeness.
- For classical first-order logic, the two are equivalent (completeness of first-order logic
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