Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects,...

involvement of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and...

structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof, a kind of proof whose semantic...

constructive and non-constructive proofs have been presented as "Cantor's proof." The popularity of presenting a non-constructive proof has led to a misconception...

computability theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include: What...

In mathematical logic, a proof calculus or a proof system is built to prove statements. A proof system includes the components: Formal language: The set...

Mathematical proof Proof assistant Proof calculus Proof theory Proof (truth) De Bruijn factor Kassios, Yannis (February 20, 2009). "Formal Proof" (PDF). cs...

Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic...

A consistency proof is a mathematical proof that a particular theory is consistent. The early development of mathematical proof theory was driven by the...

used to arrive at answers to many of the questions posed to them. In theory, the proof by exhaustion method can be used whenever the number of cases is finite...

theoretic ideas from Iwasawa theory, and other 20th-century techniques which were not available to Fermat. The proof's method of identification of a...

for example, in the proof that there is no free complete lattice on three or more generators. The paradoxes of naive set theory can be explained in terms...

In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction used to show that...

Tarski–Grothendieck set theory. PhoX – A proof assistant based on higher-order logic which is eXtensible. Prototype Verification System (PVS) – a proof language and...

where a proof is analytic if it does not go beyond its subject matter (Sebastik 2007). In proof theory, an analytic proof has come to mean a proof whose...

treated by the theory of cardinal numbers, which Cantor began. Georg Cantor published this proof in 1891,: 20–  but it was not his first proof of the uncountability...

the concept in terms of proofs and via models. The study of the syntactic consequence (of a logic) is called (its) proof theory whereas the study of (its)...

the comment that "if proof theory is about the sacred, then model theory is about the profane". The applications of model theory to algebraic and Diophantine...

elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make...

Alonzo Church Intuitionistic type theory of Per Martin-Löf Most computerized proof-writing systems use a type theory for their foundation. A common one...

its original proof Mathematical induction and a proof Proof that 0.999... equals 1 Proof that 22/7 exceeds π Proof that e is irrational Proof that π is irrational...

assert something currently not known in number theory. A proof would have to be a mathematical proof, assuming both the algorithm and specification are...

This article gives a sketch of a proof of Gödel's first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical...

logic, and in particular proof theory, a proof procedure for a given logic is a systematic method for producing proofs in some proof calculus of (provable)...

= 1445. Proof by counterexample is a form of constructive proof, in that an object disproving the claim is exhibited. In social choice theory, Arrow's...

theoretical computer science, and specifically proof theory and computational complexity theory, proof complexity is the field aiming to understand and...

type theory on the principles of mathematical constructivism. Constructivism requires any existence proof to contain a "witness". So, any proof of "there...

deducing rules. This formalization led to proof theory, which allows proving general theorems about theorems and proofs. In particular, Gödel's incompleteness...

Gentzen's consistency proof is a result of proof theory in mathematical logic, published by Gerhard Gentzen in 1936. It shows that the Peano axioms of...

theorems. The subject of logic, in particular proof theory, formalizes and studies the notion of formal proof. In some areas of epistemology and theology...