First order classes of groups having no groups with a given property

Nata\v sa Bo\v zovi\'c

Abstract: A result of Miller [8], that there exists a finitely axiomatizable theory having no nontrivial models with isolvable word problem, is generalized. It is proved here that for every strong hereditary property $P$ of $fp$ group there exist a finitely axiomatizable first-order theory $\Cal I(P)$ having no nontrivial models that enjoy $P$.

Classification (MSC2000): 20F10; 03C65

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