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Difference between revisions of "Elementary equivalence"

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(Start article: Elementary equivalence)
 
(cite Hodges (2008))
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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.   
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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====
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*  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:

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=39826