Parametric groups of definable automorphisms of strongly constructive models (Q546226)

The author defines a notion of parametric group of definable automorphisms of a structure (these are groups of automorphisms given by a single formula \(\varphi(\overline p,x,y)\) where \(\overline p\) runs over all tuples in the structure of appropriate size) and describes the class of such groups for the case of strongly constructive (decidable) structures. This class of groups coincides with the class of intersections of nested families of uniformly strongly constructive groups. It is also proven as a corollary that each strongly constructive group is isomorphic to the group of all definable automorphisms of an appropriate strongly constructive structure, and if such a group is finitely generated then one can take such a structure with finite signature.