Completion closed algebras and models of Peano arithmetic
Petr Hájek · Czech digital mathematics library · 1981
Each model M of PA determines two completion closed algebras: the system of all sets of natural*numbers parametrically and nonparametrieally coded in M respectively.This* paper is devoted to the study of models for which these two systems coincide.They are called thrifty models.A general existence theorem is proved which implies e.g. that in each countable nonstandard model of PA the class of all initial segments that are models of PA is symbiotic with the class of all models that are thrifty models of PA.