Some Problems in the Theory of Constructive Models

			S.S. Goncharov

We discuss results and related open problems in the theory
of constructive models in the following four directions:

1. existence problems for constructivizations of models with given properties

2. description of models of infinite algorithmic dimension and stable models  
   for different kinds of equivalences between constructivizations

3. existence problems for decidable, arithmetic, and hyperarithmetic models 
   in the case of theories with small number of countable models

4. computable classes of constructivizations of models, index sets,
   Roger's semilattices

References

1. Handbook on Recursive Mathematics, V. 1--2, Elsevier, Amsterdam, 1998.

2. Ershov, Yu. L., Decidability Problems and Constructive Models,
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3. Ershov, Yu. L., Definability and Computability
   (Siberian School of Algebra and Logic) Plenum, New York, 1996.

4. Ershov, Yu. L. and Goncharov, S. S., Constructive Models (Siberian School 
   of Algebra and Logic) Kluwer Academic/Plenum Publishers, 1999 [to appear].

5. Goncharov, S. S., Countable Boolean Algebras and Decidability
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6. Peretyat'kin, M. G., Finitely Axiomatizable Theories
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