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All Logic and Foundations

Proved results about formal systems, provability and the limits of what a system of axioms can settle. Belongs here: foundational theorems such as those establishing incompleteness or independence. Does not belong here: results in an ordinary branch that happen to be proved by formal methods.

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1850 1

All Logic and Foundations

90 entries

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Proved By (Other Fields)

Ax-Kochen Theorem

Baker-Gill-Solovay Theorem

Banach-Tarski Paradox

Barwise Compactness Theorem

Beth Definability Theorem

Blum's Speedup Theorem

Borel Determinacy Theorem

Bourbaki-Witt Theorem

Cantor's Theorem

Cantor-Schroder-Bernstein Theorem

Church's Theorem

Cohen's Independence Theorem

Compactness Theorem

Conservativity Theorem

Constructive Proof

Cook-Levin Theorem

Craig Interpolation Theorem

Cut-Elimination Theorem (Gentzen's Hauptsatz)

De Morgan's Laws

Deduction Theorem

Diaconescu's Theorem

Diagonal Lemma

Easton's Theorem

Ehrenfeucht-Fraisse Theorem

Entscheidungsproblem

Fodor's Lemma

Fraisse's Theorem

Frege's Theorem

Friedberg-Muchnik Theorem

Fundamental Theorem of Equivalence Relations

Fundamental Theorem of Topos Theory

Gabbay's Separation Theorem

Gentzen's Consistency Proof

Gödel's Completeness Theorem

Gödel's Incompleteness Theorems

Goodstein's Theorem

Greibach's Theorem

Herbrand's Theorem

Immerman-Szelepcsenyi Theorem

Kamp's Theorem

Kleene's Recursion Theorem

Konig's Lemma

Konig's Theorem (Set Theory)

Ladner's Theorem

Lawvere's Fixed-Point Theorem

Lindström's Theorem

Loeb's Theorem

Loewenheim-Skolem Theorem

Los's Theorem

Los-Tarski Theorem