Provable
51Morse–Kelley set theory — In the foundation of mathematics, Morse–Kelley set theory (MK) or Kelley–Morse set theory (KM) is a first order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG). While von Neumann–Bernays–Gödel set theory …
52List of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …
53debt — n [Old French dette, ultimately from Latin debita, plural of debitum debt, from neuter of debitus, past participle of debere to owe] 1: something owed: as a: a specific sum of money or a performance due another esp. by agreement (as a loan… …
54Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …
55First-order logic — is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less… …
56Theorem — The Pythagorean theorem has at least 370 known proofs[1] In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements …
57Entailment — For other uses, see Entail (disambiguation). In logic, entailment is a relation between a set of sentences (e.g.,[1] meaningfully declarative sentences or truthbearers) and a sentence. Let Γ be a set of one or more sentences; let S1 be the… …
58Philosophy of mathematics — The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of …
59Consistency — For other uses, see Consistency (disambiguation). In logic, a consistent theory is one that does not contain a contradiction.[1] The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a …
60Hilbert's tenth problem — is the tenth on the list of Hilbert s problems of 1900. Its statement is as follows:Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it… …
