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.
See also
References
- ↑ Roman Kossak, 2004 Nonstandard Models of Arithmetic and Set Theory American Mathematical Soc.
Mathematical logic |
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| General |
- Formal language
- Formation rule
- Formal proof
- Formal semantics
- Well-formed formula
- Set
- Element
- Class
- Classical logic
- Axiom
- Rule of inference
- Relation
- Theorem
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- Type theory
- Symbol
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- Theory
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| Systems |
- Formal system
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- Natural deduction
- Sequent calculus
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| Traditional logic |
- Proposition
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- Argument
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- Syllogism
- Square of opposition
- Venn diagram
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Propositional calculus
and Boolean logic |
- Boolean functions
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| Predicate logic |
- First-order
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- Monadic predicate calculus
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| Naive set theory |
- Set
- Empty set
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- Countable set
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| Set theory |
- Foundations of mathematics
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- General set theory
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| Model theory |
- Model
- Interpretation
- Non-standard model
- Finite model theory
- Truth value
- Validity
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| Proof theory |
- Formal proof
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- Syntax
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Computability
theory |
- Recursion
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- Church–Turing thesis
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 | Original source: https://en.wikipedia.org/wiki/Non-standard model. Read more |
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