Formula omitted] and induction principles in model theory

Abstract

We examine the reverse mathematics of aspects of basic classical and effective model theory, including: existence of homogeneous and saturated models, different type-amalgamation properties, the preorder of models under elementary embeddability, and existence of indiscernibles. Most theorems are equivalent to RCA0, WKL0, or ACA0. Some, however, exhibit peculiar strengths such as ¬WKL0∨ACA0 and WKL0∨IΣ20 over RCA0.