Non-standard model

See also Interpretation (logic)

In model theory, a discipline within mathematical logic, a non-standard model is a model of a theory that is not isomorphic to the intended model (or standard model). If the intended model is infinite and the language is first-order, then the Löwenheim-Skolem theorems guarantee the existence of non-standard models. The non-standard models can be chosen as elementary extensions or elementary substructures of the intended model.

Non-standard models are studied in set theory, non-standard analysis, and non-standard model of arithmetic.

This mathematical logic-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Model theory Mathematical logic stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем сделать НИР Big Rivers Regional Trail Career Assessment Center Look at other dictionaries: Non-standard model of arithmetic — In mathematical logic, a nonstandard model of arithmetic is a model of (first order) Peano arithmetic that contains nonstandard numbers. The standard model of arithmetic consists of the set of standard natural numbers {0, 1, 2, …}. The elements… …   Wikipedia Non-standard cosmology — Physical cosmology Universe · Big Bang …   Wikipedia Non-standard analysis — Abraham Robinson Gottfried Wilhelm Leibniz argued tha …   Wikipedia Standard Model (mathematical formulation) — For a basic description, see the article on the Standard Model .This is a detailed description of the standard model (SM) of particle physics. It describes how the leptons, quarks, gauge bosons and the Higgs particle fit together. It gives an… …   Wikipedia Standard Model — The Standard Model of particle physics is a theory that describes three of the four known fundamental interactions together with the elementary particles that take part in these interactions. These particles make up all matter in the universe… …   Wikipedia Non-standard arithmetic — In mathematical logic, a nonstandard model of arithmetic is a model of (first order) Peano arithmetic that contains nonstandard numbers. The standard model of arithmetic consists of the set of standard natural numbers {0, 1, 2, hellip;}. The… …   Wikipedia Standard Model (cryptography) — In cryptography the standard model is the model of computation in which the adversary is only limited by the amount of time and computational power available. Other names used are bare model and plain model.Cryptographic schemes are usually based …   Wikipedia Arithmétique non standard — En logique mathématique, un modèle non standard de l arithmétique est un modèle du premier ordre utilisant les axiomes de Peano qui contient les nombres non standards. Le modèle standard de l arithmétique contient l ensemble des nombres naturels… …   Wikipédia en Français Noncommutative standard model — In theoretical particle physics, the non commutative Standard Model, mainly due to the French mathematician Alain Connes, uses his noncommutative geometry to devise an extension of the Standard Model to include a modified form of general… …   Wikipedia Criticism of non-standard analysis — Non standard analysis and its offshoot, non standard calculus, have been criticized by several authors. The evaluation of non standard analysis in the literature has varied greatly. Joseph Dauben described it as a scientific revolution, while… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”