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]
YouTube Encyclopedic
-
1/3Views:31 470791 2892 241
-
Saul Kripke "Non-Standard Models and Gödel's Theorem"
-
CERN: The Standard Model Of Particle Physics
-
Math 1342 - Statistics: Normal Distribution (non-standard)
Transcription
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.
| General | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Theorems (list) and paradoxes | |||||||||
| Logics |
| ||||||||
| Set theory |
| ||||||||
| Formal systems (list), language and syntax |
| ||||||||
| Proof theory | |||||||||
| Model theory | |||||||||
| Computability theory | |||||||||
| Related | |||||||||
This page was last edited on 1 July 2021, at 17:56