Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.CompleteType.nonempty_iff
∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w}, Nonempty (T.CompleteType α) ↔ T.IsSatisfiable- Defined in
- Mathlib.ModelTheory.Types
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.univproof · cited by 3,945
- FirstOrder.Languagestatement and proof · cited by 1,084
- IsEmptyproof · cited by 759
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.Sentenceproof · cited by 127
- FirstOrder.Language.withConstantsproof · cited by 108
- Set.nonempty_iff_ne_emptyproof · cited by 96
- Set.union_emptyproof · cited by 78
- FirstOrder.Language.lhomWithConstantsproof · cited by 39
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