Theorems · Theorem · field theory
Field.nonempty_iff
∀ {α : Type u}, Nonempty (Field α) ↔ IsPrimePow (Cardinal.mk α)There is a field structure on type if and only if its cardinality is a prime power.
- Defined in
- Mathlib.FieldTheory.Cardinality
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Cardinalstatement · cited by 2,598
- Fintype.cardproof · cited by 1,386
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.aleph0proof · cited by 521
- Infiniteproof · cited by 352
- LT.lt.not_geproof · cited by 305
- Cardinal.mk_fintypeproof · cited by 81
- IsPrimePowstatement and proof · cited by 77
- Cardinal.natCast_lt_aleph0proof · cited by 47
- fintypeOrInfiniteproof · cited by 14
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