Theorems · Definition · order theory

HahnSeries.finiteArchimedeanClassOrderIso

(Γ : Type u_1) →
  (R : Type u_2) →
    [inst : LinearOrder Γ] →
      [inst_1 : LinearOrder R] →
        [inst_2 : AddCommGroup R] →
          [inst_3 : IsOrderedAddMonoid R] →
            [Archimedean R] → [Nontrivial R] → FiniteArchimedeanClass (Lex (HahnSeries Γ R)) ≃o Γ

For Archimedean coefficients, there is a correspondence between finite archimedean classes and HahnSeries.orderTop without the top element.

Defined in

Mathlib.RingTheory.HahnSeries.Lex

Cited by

3 results in Mathlib

Foundations

Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderLinearOrderAddCommGroupIsOrderedAddMonoidArchimedeanNontrivial