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Proof Theory

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Proof theory
Realizability
Epsilon calculus
Analytic proof
Bachmann–Howard ordinal
Bounded quantifier
Church–Kleene ordinal
Completeness
Completeness of atomic initial sequents
Conservative extension
Conservativity theorem
Consistency
Curry–Howard correspondence
Cut-elimination theorem
Decidability (logic)
Decidable sublanguages of set theory
Deduction theorem
Deductive system
Deep inference
Dialectica interpretation
Disjunction and existence properties
Elementary function arithmetic
Extension by definitions
Fast-growing hierarchy
Feferman–Schütte ordinal
Formal proof
Friedman translation
Gentzen's consistency proof
Geometry of interaction
Gödel's completeness theorem
Gödel–Gentzen negative translation
Gödel's incompleteness theorems
Original proof of Gödel's completeness theorem
Hardy hierarchy
Herbrand's theorem
Hilbert system
Hilbert's program
Independence (mathematical logic)
Interpretability
Judgment (mathematical logic)
Lambda-mu calculus
Large countable ordinal
Mathematical fallacy
Mathematical induction
Metalanguage
Natural deduction
NuPRL
Ω-consistent theory
Ordinal analysis
Ordinal notation
Paraconsistent mathematics
Peano-Russell notation
Presburger arithmetic
Primitive recursive functional
Proof (truth)
Proof calculus
Proof mining
Proof net
Proof procedure
Proof-theoretic semantics
Provability logic
Psi0(Omega omega)
Pure type system
Reverse mathematics
Self-verifying theories
Sequent
Sequent calculus
Setoid
Slow-growing hierarchy
Soundness
Structural proof theory
Structural rule
Takeuti's conjecture
Tolerant sequence
Turnstile (symbol)
Undecidable problem
Veblen function
Weak interpretability
Rule of inference
Law of thought
List of rules of inference
Admissible rule
Biconditional elimination
Biconditional introduction
Case analysis
Commutativity of conjunction
Conjunction introduction
Constructive dilemma
Contraposition (traditional logic)
Conversion (logic)
De Morgan's laws
Destructive dilemma
Dictum de omni et nullo
Disjunction elimination
Disjunction introduction
Disjunctive syllogism
Double negative elimination
Generalization (logic)
Hypothetical syllogism
Independence of premise
Law of identity
Law of excluded middle
Modus ponens
Modus tollens
Modus ponendo tollens
Negation as failure
Obversion
Principle of contradiction
Principle of explosion
Proof by contradiction
Proof by contrapositive
Resolution (logic)
Simplification
Transposition (logic)
Universal instantiation
Substructural logic
Affine logic
Bunched logic
Linear logic
Noncommutative logic
Relevance logic
Strict logic