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...

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

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

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

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

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

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

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...

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

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)...

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...

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...

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

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...

striking claimed application of the theory is to provide a proof for various outstanding conjectures in number theory, in particular the abc conjecture...

uncountability proof, which differs from the more familiar proof using his diagonal argument. Cantor introduced fundamental constructions in set theory, such as...

interpreted as a proof within a first-order set theory, such as ZFC, Dedekind's categoricity proof for PA shows that each model of set theory has a unique...

by any first-order theory (such as the integers). A simpler, but related, problem is proof verification, where an existing proof for a theorem is certified...

Mathematical proof Direct proof Reductio ad absurdum Proof by exhaustion Constructive proof Nonconstructive proof Tautology Consistency proof Arithmetization...

continued looking for a more general proof of the consistency of classical mathematics using methods from proof theory. A strongly negative answer to whether...

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...

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

Proof-theoretic semantics is a branch of proof theory and an approach to the semantics of logic that attempts to locate the meaning of propositions and...

set, the continuous image of a Polish space Analytic proof, in structural proof theory, a proof whose structure is simple in a special way Analytic tableau...

theory Illuminationist philosophy Logical atomism Logical holism Logicism Modal fictionalism Nominalism Polylogism Pragmatism Preintuitionism Proof theory...

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

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...

the foundations of mathematics (particularly proof theory). He adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented...