A Transfer Principle for Simple Properties of Theories
Mark E. Nadel · Proceedings of the American Mathematical Society · 1976
A notion of simple property of theories is introduced and it is shown that if ${\text {P}}$ is a simple property of theories, $A$ countable admissible, and $M$ a structure in $A$, then ${\operatorname {Th} _A}(M)$ has property ${\text {P}}$ iff ${\operatorname {Th} _{\infty \omega }}(M)$ has property ${\text {P}}$.