A transfer principle for simple properties of theories

Abstract

A notion of simple property of theories is introduced and it is shown that if P {\text {P}} is a simple property of theories, A A countable admissible, and M M a structure in A A , then Th A ( M ) {\operatorname {Th} _A}(M) has property P {\text {P}} iff Th ∞ ω ( M ) {\operatorname {Th} _{\infty \omega }}(M) has property P {\text {P}} .