Provable
31Heyting algebra — In mathematics, Heyting algebras are special partially ordered sets that constitute a generalization of Boolean algebras, named after Arend Heyting. Heyting algebras arise as models of intuitionistic logic, a logic in which the law of excluded… …
32bankruptcy — /bangk rupt see, reuhp see/, n., pl. bankruptcies. 1. the state of being or becoming bankrupt. 2. utter ruin, failure, depletion, or the like. [1690 1700; BANKRUPT + CY] * * * Status of a debtor who has been declared by judicial process to be… …
33Axiom of choice — This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band). In mathematics, the axiom of choice, or AC, is an axiom of set theory stating that for every family of nonempty sets there exists a family of …
34propositional calculus — Logic. See sentential calculus. [1900 05] * * * Formal system of propositions and their logical relationships. As opposed to the predicate calculus, the propositional calculus employs simple, unanalyzed propositions rather than predicates as its… …
35Propositional calculus — In mathematical logic, a propositional calculus or logic (also called sentential calculus or sentential logic) is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules… …
36Reverse mathematics — is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. The method can briefly be described as going backwards from the theorems to the axioms. This contrasts with the ordinary… …
37mathematics, foundations of — Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods. It began with Euclid s Elements as an inquiry into the logical and philosophical basis of mathematics in essence, whether the axioms of any system… …
38Gödel's completeness theorem — is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first order logic. It was first proved by Kurt Gödel in 1929. A first order formula is called logically valid if… …
39Soundness — In mathematical logic, a logical system has the soundness property if and only if its inference rules prove only formulas that are valid with respect to its semantics. In most cases, this comes down to its rules having the property of preserving… …
40Natural deduction — In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the natural way of reasoning. This contrasts with the axiomatic systems which instead use… …
