Fundamental theorem of ultraproducts
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
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| gptkbp:alsoKnownAs |
gptkb:Łoś's_theorem
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| gptkbp:appliesTo |
ultraproducts
ultrapowers |
| gptkbp:citation |
Łoś, Jerzy (1955). "Quelques remarques, théorèmes et problèmes sur les classes définissables d'algèbres". In Mathematical interpretation of formal systems.
|
| gptkbp:field |
gptkb:logic
model theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Fundamental theorem of ultraproducts
|
| gptkbp:implies |
elementary equivalence of ultraproducts
|
| gptkbp:introduced |
gptkb:Jerzy_Łoś
|
| gptkbp:introducedIn |
1955
|
| gptkbp:state |
A first-order sentence is true in an ultraproduct if and only if it is true in 'almost all' of the structures, with respect to the ultrafilter.
|
| gptkbp:usedIn |
gptkb:algebra
gptkb:set_theory gptkb:nonstandard_analysis model theory |
| gptkbp:bfsParent |
gptkb:Łoś's_theorem
|
| gptkbp:bfsLayer |
6
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