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orderable field

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  • Real closed field — In mathematics, a real closed field is a field F in which any of the following equivalent conditions are true:#There is a total order on F making it an ordered field such that, in this ordering, every positive element of F is a square in F and… …   Wikipedia

  • Formally real field — In mathematics, a formally real field in field theory is a field that shares certain algebraic properties with the real number field. A formally real field F may be characterized in any of the following equivalent ways:* −1 is not a sum of… …   Wikipedia

  • Group ring — This page discusses the algebraic group ring of a discrete group; for the case of a topological group see group algebra, and for a general group see Group Hopf algebra. In algebra, a group ring is a free module and at the same time a ring,… …   Wikipedia

  • Cyclic order — In mathematics, a cyclic order is a way to arrange a set of objects in a circle.[nb] Unlike most structures in order theory, a cyclic order cannot be modeled as a binary relation a < b . One does not say that east is more clockwise than west.… …   Wikipedia

  • Quark Framework — CAL Paradigm(s) functional, non strict, modular Appeared in 2004 Designed by Luke Evans, Bo Ilic (Business Objects) Typing discipline static, strong …   Wikipedia

  • Reverse 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… …   Wikipedia

  • Oracle Exadata — is a database appliance with support for both OLTP and OLAP workloads. It was initially designed in collaboration between Oracle Corporation and Hewlett Packard where Oracle designed the database, operating system (based on the Oracle Linux… …   Wikipedia

  • Infinitary logic — Those unfamiliar with mathematical logic or the concept of ordinals are advised to consult those articles first. An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Some infinitary logics may have… …   Wikipedia

  • Perfect graph — The Paley graph of order 9, colored with three colors and showing a clique of three vertices. In this graph and each of its induced subgraphs the chromatic number equals the clique number, so it is a perfect graph. In graph theory, a perfect… …   Wikipedia

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