Amador Martin-Pizarro, Daniel Palacín
The purpose of this simple note is to provide elementary model-theoretic proofs to some existing results on sumset phenomena and IP sets, motivated by Hrushovski's work on the stabilizer theorem.
Amador Martin-Pizarro, Daniel Palacín
This paper contains 3 sections, 13 theorems, 28 equations.
Theorem 1
Let $G$ be a definable group with an $\emptyset$-type-definable left-translation ideal $\mathcal{I}$ of definable subsets of $G$. Assume that $\mathcal{I}$ is indiscernibly prime (see Definition D:S1). The following conditions are equivalent for every elementary submodel $M$: Moreover, if the second condition holds for some elementary submodel $M$, then it holds for every elementary submodel.
