Sufficient conditions for Axiom 10
Patrick Maher · 1993
This appendix proves that when Axioms 1–8 are satisfied, then the following conditions are jointly sufficient (but not necessary) for Axiom 10: (i) There are “best” and “worst” acts; that is, there exist k , l ∈ D such that, for all f ∈ D , k ≲ f ≲ l . (ii) For all f ∈ D , if k ≲ f or f ≲ l , then there exists h ∈ ∪ L such that h ≲ f or f ≲ h (respectively). As in Appendix B, we here use the fact that the set of simple acts in D is ∪ L .