Presentations of Structures in Admissible Sets

Abstract

We consider copies and constructivizations of structures in admissible sets. In the first section we survey results about copies of countable structures in hereditary finite superstructures and definability (so called syntactical conditions of intrinsically computable properties) and state some conjectures about the uncountable case. The second section is devoted to constructivizations of uncountable structures in “simplest” uncountable admissible sets (more precisely, in hereditary finite superstructures over the models of c-simple theories). The third section contains some results on constructivizations of admissible sets within themselves.