Difference between revisions of "Elementary equivalence"
From Encyclopedia of Mathematics
(Start article: Elementary equivalence) |
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{{TEX|done}}{{MSC|03C07}} | {{TEX|done}}{{MSC|03C07}} | ||
| − | The relationship between models for a first-order language $L$ for which the sentences of $L$ have the same truth values in the models. | + | The relationship between models for a first-order language $L$ for which the sentences of $L$ have the same truth values in the models. Such models are said to be "elementarily equivalent" or "first-order equivalent". |
See: | See: | ||
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* [[Keisler-Shelah isomorphism theorem]] | * [[Keisler-Shelah isomorphism theorem]] | ||
* [[Abstract algebraic logic]] | * [[Abstract algebraic logic]] | ||
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| + | ====References==== | ||
| + | * Hodges, Wilfrid. "Model theory" Encyclopaedia of Mathematics and Its Applications '''42'''. Cambridge University Press (2008) ISBN 978-0-521-06636-5 {{ZBL|1139.03021}} | ||
Revision as of 19:27, 26 November 2016
2020 Mathematics Subject Classification: Primary: 03C07 [MSN][ZBL]
The relationship between models for a first-order language $L$ for which the sentences of $L$ have the same truth values in the models. Such models are said to be "elementarily equivalent" or "first-order equivalent".
See:
- Fraïssé characterization of elementary equivalence
- Keisler-Shelah isomorphism theorem
- Abstract algebraic logic
References
- Hodges, Wilfrid. "Model theory" Encyclopaedia of Mathematics and Its Applications 42. Cambridge University Press (2008) ISBN 978-0-521-06636-5 Zbl 1139.03021
How to Cite This Entry:
Elementary equivalence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Elementary_equivalence&oldid=39816
Elementary equivalence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Elementary_equivalence&oldid=39816