...PUBLICATIONS...

**SCIENTIFIC PUBLICATIONS**

*Directions:* Model theory, Constructive models, Boolean algebras,
Algorithmic problems of Logic, Finitely axiomatizable theories, Structure of
first-order Predicate Calculus (structure of Lindenbaum algebra and generalized
Lindenbaum algebra of Predicate Calculus)

*Top results:*

Invited 45-minute address at International Congress of Mathematicians, Berkeley
(USA), August 1986. Title: "*Finitely Axiomatizable Theories"*

Monograph Finitely Axiomatizable Theories. Plenum Publ. Co., New York, London, Moscow. 1997, 294 p.

*List of publications:*

1. Peretyat'kin M.G. Strongly constructive models and numerations of Boolean
algebra of recursive sets. Algebra and Logic, 1971, v.10, No 5, p.535--557
(Russian, there is translation in English)

2. Peretyat'kin M.G. On strongly constructive models. Abstracts of conference of
post-graduates and students of Novosibirsk State University Novosibirsk, Russia,
1971, p.9--10

3. Peretyat'kin M.G. Every recursively enumerable extensions of theory of linear
order has a constructive model. Algebra and Logic, 1973, v.12, No 2, p.211--219
(Russian, there is translation in English)

4. Peretyat'kin M.G. Strongly constructive model without constructive elementary
submodels and extensions. Algebra and Logic, 1973, v.12, No 3, p.312--322
(Russian, there is translation in English)

5. Peretyat'kin M.G. On complete theories with finite number of countable
models. Algebra and Logic, 1973, v.12, No 5, p.550--576 (Russian, there is
translation in English)

6. Peretyat'kin M.G. Constructive models. Ph.Dr. Thesis, Novosibirsk, Russia,
Novosibirsk State University, 149 pp. (Russian)

7. Peretyat'kin M.G. Constructive models. Abstract of Ph.Dr. Thesis,
Novosibirsk, Russia, Novosibirsk State University, 1974, p.1--14 (Russian)

8. Peretyat'kin M.G. (jointly with I.Korec and W.Rautenberg). Definability in
structures of finite valency. Fundamenta mathematicae, LXXXI, 1974, p.173--181

9. Peretyat'kin M.G. An example of a decidable theory without countable
constructive models. Proceedings of conference of teachers of Kazakh State
University, Almaty, Kazakhstan, 1975, p.292 (Russian)

10. Peretyat'kin M.G. Criteria of strong constructivizability of homogeneous
models. Algebra and Logic, 1978, v.17, No 4, p.436--454 (Russian, there is
translation in English)

11. Peretyat'kin M.G. On theories with three countable models. Algebra and
Logic, 1980, v.19, No 2, p.224--233 (Russian, there is translation in English)

12. Peretyat'kin M.G.. On finitely axiomatizable theories. V All-Union
conference on Mathematical Logic (abstracts), Novosibirsk, Russia, 1979, p.119
(Russian)

13. Peretyat'kin M.G. Complexity of some classes of sentences. V All-Union
conference on Mathematical Logic (abstracts), Novosibirsk, Russia, 1979, p.120
(Russian)

14. Peretyat'kin M.G. An example of omega-one categorical complete finitely
axiomatizable theory. Algebra and Logic, 1980, v.19, No 3, p.314--347 (Russian,
there is translation in English)

15. Peretyat'kin M.G. Computations on Turing Machines in finitely axiomatizable
theories. Algebra and Logic, 1982, v.21, No 4, p.410--441 (Russian, there is
translation in English)

16. Peretyat'kin M.G. Finitely axiomatizable totally transcendental theories.
Transactions of Institute of Mathematics of Siberian Branch of Russian Academy
of Sciences, v.2, Siberian Branch of Publishing Company "Science", Novosibirsk,
Russia, 1982, p.88--135 (Russian)

17. Peretyat'kin M.G. On constructive models of finitely axiomatizable theories.
Investigations on Constructive Models, Proceedings of Kazakh State University,
Almaty, Kazakhstan, 1982, p.63--72 (Russian)

18. Peretyat'kin M.G. On finitely axiomatizable theories with finite models. VI
All-Union Conference on Mathematical Logic (abstracts), Tbilisi, Georgia, 1982,
p.141 (Russian)

19. Peretyat'kin M.G. Finitely axiomatizable theories. Doctor's Thesis,
Novosibirsk, Russia, Institute of Mathematics, 1982, 215 p. (Russian)

20. Peretyat'kin M.G. Finitely axiomatizable theories. Abstract of Doctor's
Thesis, Novosibirsk, Russia, Institute of Mathematics, 1983, p.1--21 (Russian)

21. Peretyat'kin M.G. Expressibility of finitely axiomatizable theories.
International Congress of Mathematicians (abstracts) Warszawa, Poland, 1983,
p.137 (Russian)

22. Peretyat'kin M.G. Standard form of countably categorical complete finitely
axiomatizable theories. Applied Aspects of Mathematical Physic and Functional
Analysis, Almaty, Publishing Co "Science of Kazakhstan", 1985, p.113--118
(Russian)

23. Peretyat'kin M.G. Finitely axiomatizable theories. Proceedings of
International Congress of Mathematicians, Berkeley, California, USA, 1986,
volume 1, p.322--330 (Russian, there is translation in English)

24. Peretyat'kin M.G. Expressive possibilities of finitely axiomatizable
theories. IX All-Union Conference on Mathematical Logic (abstracts),
St.Petersburg, Russia, 1988, p.128 (Russian)

25. Peretyat'kin M.G. Similarity of properties of finitely axiomatizable
theories and finitely axiomatizable theories. Soviet Math. Docl., v.308, No 4,
1989, p.788--791 (Russian, there is translation in English)

26. Peretyat'kin M.G. Generalization intelligence in predicate logic. IX
Inter-University Conference on Mathematics and Mechanics, part.1, Mathematic
(abstracts), Almaty, Kazakhstan, 1989, p.170 (Russian)

27. Peretyat'kin M.G. Two theorems on finitely axiomatizable theories.
International Conference in Memory of Academician Maltsev, Model Theory and
Algebraic Systems (abstracts), Novosibirsk, Russia, 1989, p.99

28. Peretyat'kin M.G. Similarity of the properties of recursively enumerable and
finitely axiomatizable theories. Soviet Math Docl., 40, No 2, 1990, p.372--375

29. Peretyat'kin M.G. Disjunction phenomenon for L-universal classes.
International Colloquium on Model Theory (theses), Karaganda, Kazakhstan, June
1990, p. 37--38

30. Peretyat'kin M.G., Finitely axiomatizable theories. Proceedings of
International Congress of Mathematicians, Berkeley, California, USA,1986, volume
1, p. 322--330 (Russian). English translation in: Amer. Math. Soc. Transl., (2)
v.147, 1990, p.11--19.

31. Peretyat'kin M.G. On Boolean algebras over arithmetical hierarchy. X
All-Union Conference on Mathematical Logic (abstracts), Almaty, Kazakhstan,
1990, p.127 (Russian)

32. Peretyat'kin M.G. Uncountably categorical quasisuccession of Morley rank 3.
Algebra and Logic, 1991, v.30, No 1, p.74--89 (Russian, there is translation in
English)

33. Peretyat'kin M.G. Isomorphism of Predicate Calculi over the superlist.
International Conference on Algebra in Memory of A.I.Shirshov (abstracts),
Barnaul, Russia, 1991, p.105 (Russian, there is translation in English)

34. Peretyat'kin M.G. Semantic universal classes of models. Algebra and Logic,
1991, v.30, No 4, p.414--434 (Russian, there is translation in English)

35. Peretyat'kin M.G.. Analogues of Rice theorem for semantic classes of
sentences. Algebra and Logic, 1991, v.30, No 5, p.517--539 (Russian, there is
translation in English)

36. Peretyat'kin M.G. Semantic universality of theory over superlist. Algebra
and Logic, 1992, v.31, No 1, p.47--73 (Russian, there is translation in English)

37. Peretyat'kin M.G. Semantical significance of formulas in the classical
predicate logic. Contemporary Mathematics, 1992, No 131, part 3, p.623--643

38. Peretyat'kin M.G. Expressive power of finitely axiomatizable theories, I.
Introduction, interpretations, reduction to graphs. Siberian Advances in
Mathematics, Allerton press, Inc., v.3, No 2, 1993, p. 153--197

39. Peretyat'kin M.G. Expressive power of finitely axiomatizable theories, II.
Rigid Quasisuccession. Siberian Advances in Mathematics, Allerton press, Inc.,
v.3, No 3, 1993, p. 123--145

40. Peretyat'kin M.G. Expressive power of finitely axiomatizable theories, III
Main Construction. Siberian Advances in Mathematics, Allerton press, Inc., v.3,
No 4, 1993, p. 131--201

41. Peretyat'kin M.G. On semantical classes of sentences with decidability
property. International Conference on Mathematical Logic (abstracts),
Novosibirsk, Russia, 1994, p.79--80 (Russian)

42. Peretyat'kin M.G. On semantic classes of sentences. Logic Colloquium 1994,
France, Clermont-Ferrand. (Abstract of the talk is published in Bulletin of
Symbolic Logic, 1995, v.1, N 2, p. 256).

43. Peretyat'kin M.G. Factorization and cut of a properties list. Algebra.
Proceedings of the III-rd International Conference on Algebra, held in
Krasnoyarsk, Russia, August 23--28, 1993 edited by Yu.L.Ershov, E.I.Khukhro,
V.M.Levchuk, N.V.Podufalov. Berlin, March 1996, p. 49.

44. Peretyat'kin M.G. Finitely Axiomatizable Theories. Plenum Publ. Co., New
York, London, Moscow. 1997, monograph, 294 p.

45. Peretyat'kin M.G. Finitely axiomatizable theories. Novosibirsk, MIOO,
Scientific Books, 1997, monograph, 318 pp. (Russian)

46. Peretyat'kin M.G.. Constructive Models of Finitely Axiomatizable Theories.
Handbook of Recursive Mathematics, Volume 1 (Recursive model theory), Elsevier
Publ., Co., 1998, p. 347--379.

47. Peretyat'kin M.G. Expressive possibilities of finitely axiomatizable
theories. International Congress of Mathematicians, Berlin, August 1998,
Abstracts, p.172.

48. Peretyat'kin M.G.. Finitely axiomatizable theories and similarity relations
Contemporary Mathematics, (2) Vol.195, 1999, p.309--346.

49. Peretyat'kin M.G. Finitely axiomatizable theories and Lindenbaum algebras of
semantic classes. Contemporary Mathematics (Computability Theory and
Applications, Current trends and Open Problems), 257, 2000, p. 221--239.

50. Peretyat'kin M.G. Polar construction of finitely axiomatizable theories.
Logic and applications, International Conference on Algebra and Logic devoted to
60-year Anniversary of Academician Yu.L.Ershov, Novosibirsk, Russia, May 4--6,
2000, p.136.

51. Peretyat'kin M.G. (jointly with Lempp S. and Solomon R.), The Lindenbaum
algebra of the theory of the class of all finite models. Journal of Mathematical
Logic, World Scientific Publishing Company and Singapore University Press, Vol.
2, No 2 (2002), pp.145--225

52. Peretyat'kin M.G. Fundamental Structures of Computer Science. Lecture
Course, Part 1 --- 161 p., Part 2 --- 261 p., Publication at Suleyman Demirel
University, Almaty, Kazakhstan, 2002 (in English).

53. Peretyat'kin M.G. Lindenbaum algebras of seven semantic classes of models.
Algebra and Logic, 24 pp., 2004 (Russian, in publication).

54. Peretyat'kin M.G. Expressive Power of First Order Predicate Logic (monograph, currently in preparation)

consisting of two following parts:

*Part 1.* Earlier constructions

Church's, Trachtenbrot's, Vaught's, Polar and Hanf's primitive constructions,
approximately 125 pages, a lot of figures;

*Part 2*. Optimal constructions

Hanf's, Radical, and the Canonical constructions, approximately 400 pages, a lot
of formal proofs and figures.

*Status:* In preparation, a few final readings and corrections is remainded

General info concerning the monograph is exhibited in this site. To look it, go
to page "Monograph" in the site.