Cohesive Powers of Computable Structures

We develop the notion of cohesive power \mathcal{B} of a computable structure \mathcal{A} over a cohesive set \mathcal{R}. In the main theorem of this paper we prove certain connections between satisfaction of different formulas and sentences in the original model \mathcal{A} and its cohesive power \mathcal{B}. We also prove various facts about cohesive powers, isomorphisms between them and consider an example in which the structure \mathcal{A} is a computable field.