Non-standard model
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).[1]
Existence
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.
Importance
Non-standard models are studied in set theory, non-standard analysis and non-standard models of arithmetic.
gollark: Anyway, the main issue I see with genetically engineering child super-soldiers is that the children can't really consent to said modification, especially if it's before they're born.
gollark: I... haven't heard about them doing that?
gollark: > If you consider the “standard of living” to be something we should make effort improve in a utilitarian philosophy senseis just assuming utilitarian philosophy is "right".
gollark: 'Tis the is-ought problem.
gollark: Somewhat more implicitly.
See also
- Interpretation (logic)
- Non-standard model of arithmetic
- Non-standard analysis
References
- Roman Kossak, 2004 Nonstandard Models of Arithmetic and Set Theory American Mathematical Soc.
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