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In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it.
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displaystyle signature theory mathcal structure model relation structures domain function algebra set symbol first-order called also universal induced interpretation sigma
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| groups | instance of | a structure consists of a set along with a collection of finitary operations and relations that are defined on it.Universal algebra studies structures that generalize the algebr… | 0.80 | text |
| rings | instance of | a structure consists of a set along with a collection of finitary operations and relations that are defined on it.Universal algebra studies structures that generalize the algebr… | 0.80 | text |
| fields | instance of | a structure consists of a set along with a collection of finitary operations and relations that are defined on it.Universal algebra studies structures that generalize the algebr… | 0.80 | text |
| vector spaces | instance of | a structure consists of a set along with a collection of finitary operations and relations that are defined on it.Universal algebra studies structures that generalize the algebr… | 0.80 | text |
| models of set theory.From the model-theoretic point of view | instance of | including foundational structures | 0.80 | text |
| structures are the objects used to define the semantics of first-order logic | instance of | including foundational structures | 0.80 | text |
| cf. also Tarski's theory of truth or Tarskian semantics.For a given theory in model theory | instance of | including foundational structures | 0.80 | text |
| a structure is called a model if it satisfies all the sentences of that theory | instance of | including foundational structures | 0.80 | text |
| that used in universal algebra | instance of | and in fact they are suitable as semantic objects both for very restricted fragments of first-order logic | 0.80 | text |
| and for second-order logic | instance of | and in fact they are suitable as semantic objects both for very restricted fragments of first-order logic | 0.80 | text |
| tuples of sorts rather than natural numbers.Vector spaces | instance of | the arities of function symbols or relation symbols must be more complicated objects | 0.80 | text |
| for example | instance of | the arities of function symbols or relation symbols must be more complicated objects | 0.80 | text |
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