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second-order arithmetic

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  • Second-order arithmetic — In mathematical logic, second order arithmetic is a collection of axiomatic systems that formalize the natural numbers and sets thereof. It is an alternative to axiomatic set theory as a foundation for much, but not all, of mathematics. The… …   Wikipedia

  • Second-order logic — In logic and mathematics second order logic is an extension of first order logic, which itself is an extension of propositional logic.[1] Second order logic is in turn extended by higher order logic and type theory. First order logic uses only… …   Wikipedia

  • Arithmetic — tables for children, Lausanne, 1835 Arithmetic or arithmetics (from the Greek word ἀριθμός, arithmos “number”) is the oldest and most elementary branch of mathematics, used b …   Wikipedia

  • Order (mathematics) — Contents 1 In algebra 2 In arithmetic 3 In analysis 4 …   Wikipedia

  • First-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… …   Wikipedia

  • List of first-order theories — In mathematical logic, a first order theory is given by a set of axioms in somelanguage. This entry lists some of the more common examples used in model theory and some of their properties. PreliminariesFor every natural mathematical structure… …   Wikipedia

  • Robinson arithmetic — In mathematics, Robinson arithmetic, or Q, is a finitely axiomatized fragment of Peano arithmetic (PA), first set out in Robinson (1950). Q is essentially PA without the axiom schema of induction. Even though Q is much weaker than PA, it is still …   Wikipedia

  • Primitive recursive arithmetic — Primitive recursive arithmetic, or PRA, is a quantifier free formalization of the natural numbers. It was first proposed by Skolem [Thoralf Skolem (1923) The foundations of elementary arithmetic in Jean van Heijenoort, translator and ed. (1967)… …   Wikipedia

  • Arithmetic logic unit — schematic symbol Cascadable 8 …   Wikipedia

  • Arithmetic coding — is a method for lossless data compression. Normally, a string of characters such as the words hello there is represented using a fixed number of bits per character, as in the ASCII code. Like Huffman coding, arithmetic coding is a form of… …   Wikipedia

  • arithmetic — arithmetically, adv. n. /euh rith meuh tik/; adj. /ar ith met ik/, n. 1. the method or process of computation with figures: the most elementary branch of mathematics. 2. Also called higher arithmetic, theoretical arithmetic. the theory of… …   Universalium

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