ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

1. Logic

1991 MS Classification: 03 Peretyat’kin, Mikhail G., Institute of Pure and Applied Mathematics, Almaty, Kazakhstan Expressive possibilities of finitely axiomatizable theories General expressibility problem of finitely axiomatizable theories in firstorder predicate logic is decided. An universal construction is described which shows that in terms of the majority of natural model-theoretic properties the expressive power of finitely axiomatizable theories is the same as that of recursively axiomatizable theories. A lot of natural questions on finitely axiomatizable theories is solved by reduction to the considerably easier case of recursively axiomatizable theories. Some intermediate construction of finitely axiomatizable theories was represented [1]. The universal construction is described [2]. References: [1] M. G. Peretyat’kin, Finitely axiomatizable theories, Proc. Intern. Congress Mathematicians, Berkeley, USA (1986), 1, 322–330 (Russian); English translation: Amer. Math. Soc. Transl. , (2) 147 (1990), 11–19. [2] M. G. Peretyat’kin, Finitely axiomatizable theories, Plenum, New York (1997), 294p.