Theorems · Definition · order theory

LocallyFiniteOrder.orderMonoidEquiv

(G : Type u_3) →
  [inst : CommGroup G] →
    [inst_1 : LinearOrder G] → [IsOrderedMonoid G] → [LocallyFiniteOrder G] → [Nontrivial G] → G ≃*o Multiplicative ℤ

Any linearly ordered abelian group that is locally finite embeds to Multiplicative ℤ.

Defined in

Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupLinearOrderIsOrderedMonoidLocallyFiniteOrderNontrivial