Results in Metalogic
Results in metalogic consist of such things as formal proofs demonstrating the consistency, completeness, and decidability of particular formal systems.
Major results in metalogic include:
- Proof of the uncountability of the set of all subsets of the set of natural numbers (Cantor's theorem 1891)
- Löwenheim–Skolem theorem (Leopold Löwenheim 1915 and Thoralf Skolem 1919)
- Proof of the consistency of truth-functional propositional logic (Emil Post 1920)
- Proof of the semantic completeness of truth-functional propositional logic (Paul Bernays 1918), (Emil Post 1920)
- Proof of the syntactic completeness of truth-functional propositional logic (Emil Post 1920)
- Proof of the decidability of truth-functional propositional logic (Emil Post 1920)
- Proof of the consistency of first order monadic predicate logic (Leopold Löwenheim 1915)
- Proof of the semantic completeness of first order monadic predicate logic (Leopold Löwenheim 1915)
- Proof of the decidability of first order monadic predicate logic (Leopold Löwenheim 1915)
- Proof of the consistency of first order predicate logic (David Hilbert and Wilhelm Ackermann 1928)
- Proof of the semantic completeness of first order predicate logic (Gödel's completeness theorem 1930)
- Proof of the undecidability of first order predicate logic (Church's theorem 1936)
- Gödel's first incompleteness theorem 1931
- Gödel's second incompleteness theorem 1931
- Tarski's undefinability theorem (Gödel and Tarski in the 1930s)
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