Vol. 37(51), pp. 51--55 (1985)
First order classes of groups having no groups with a given property
Nata\v sa Bo\v zovi\'cMatemati\v cki fakultet, Beograd, Yugoslavia
Abstract: A result of Miller , 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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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts