Mathlib Map

Theorems · Definition · logic and foundations

FirstOrder.Language.infiniteTheory

(L : FirstOrder.Language) → L.Theory

A theory indicating that a structure is infinite.

Defined in
Mathlib.ModelTheory.Syntax
Cited by
2 results in Mathlib
Foundations
Depth 16 from the axioms · uses no axioms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FirstOrder.Language.model_infiniteTheory_iff · cited by 2Language.model_infiniteTh…Cardinal.empty_infinite_Theory_isComplete · cited by 0Cardinal.empty_infinite_T…Set.range · cited by 4705Set.rangeFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Theory · cited by 154Language.TheoryFirstOrder.Language.Sentence.cardGe · cited by 3Sentence.cardGeLanguage.infiniteTheoryCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.