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finitely axiomatizable system

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  • Foundations of mathematics — is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. The search for foundations of mathematics is also a central question of the philosophy …   Wikipedia

  • Certainty — series Agnosticism Belief Certainty Doubt Determinism Epistemology Estimation Fallibilism …   Wikipedia

  • logic, history of — Introduction       the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic       There was a medieval tradition according to which the Greek philosopher …   Universalium

  • Relation algebra — is different from relational algebra, a framework developed by Edgar Codd in 1970 for relational databases. In mathematics, a relation algebra is a residuated Boolean algebra supporting an involutary unary operation called converse. The… …   Wikipedia

  • ω-consistent theory — In mathematical logic, an ω consistent (or omega consistent, also called numerically segregative[1]) theory is a theory (collection of sentences) that is not only (syntactically) consistent (that is, does not prove a contradiction), but also… …   Wikipedia

  • Ω-consistent theory — In mathematical logic, an ω consistent (or omega consistent, also called numerically segregativeW.V.O. Quine, Set Theory and its Logic ] ) theory is a theory (collection of sentences) that is not only (syntactically) consistent (that is, does not …   Wikipedia

  • Boolean algebra — This article discusses the subject referred to as Boolean algebra. For the mathematical objects, see Boolean algebra (structure). Boolean algebra, as developed in 1854 by George Boole in his book An Investigation of the Laws of Thought,[1] is a… …   Wikipedia

  • Boolean algebra (introduction) — Boolean algebra, developed in 1854 by George Boole in his book An Investigation of the Laws of Thought , is a variant of ordinary algebra as taught in high school. Boolean algebra differs from ordinary algebra in three ways: in the values that… …   Wikipedia

  • Admissible rule — In logic, a rule of inference is admissible in a formal system if the set of theorems of the system is closed under the rule. The concept of an admissible rule was introduced by Paul Lorenzen (1955).DefinitionsThe concept of admissibility, as… …   Wikipedia

  • Zermelo–Fraenkel set theory — Zermelo–Fraenkel set theory, with the axiom of choice, commonly abbreviated ZFC, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.ZFC consists of a single primitive ontological notion, that of… …   Wikipedia

  • Decidability (logic) — In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas. Logical systems such as propositional logic are decidable if membership in their… …   Wikipedia

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