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Proof Theory
edit- 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