Linear extensions of orders invariant under abelian group actions

• Autorzy: Alexander R. Pruss
• Języki publikacji: EN

Abstrakty

EN

Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under G extends to a linear order on X also invariant under G. We then discuss extensions to linear preorders when the orbit condition is not met, and show that for any abelian group acting on a set X, there is a linear preorder ≤ on the powerset 𝓟X invariant under G and such that if A is a proper subset of B, then A < B (i.e., A ≤ B but not B ≤ A).

Kategorie tematyczne

• 06F99: None of the above, but in this section
• 06A05: Total order
• 06A06: Partial order, general

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 137
• Numer: 1
• Strony: 117-125

Daty

wydano

2014

Twórcy

autor

Alexander R. Pruss

• Department of Philosophy, Baylor University, One Bear Place #97273, Waco, TX 76798-7273, U.S.A.

Identyfikatory

DOI

10.4064/cm137-1-8