Petersburg Department of Steklov Institute of Mathematics

PREPRINT 06/2000

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This preprint was accepted 2000
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N.A.Shanin. A sketch of a finitary version of mathematical

CONTENTS.1. On basic ideas of finitary mathematics.- 2.
theories of natural numbers and arithmetical 
 algorithms as an `environment of
modeling' finitary theories of constructively definable objects
of various types.- 3. Approach of R.L.Goodstein to a
construction of 
finitary versions of initial parts of mathematical analysis.- 4.
Finitary completions  of elementary metric and countably metric
spaces as 
finitary counterparts  of function spaces of classical mathematics.-
5. On the theorems 
of finitary mathematics that have the form of majorants of
theorems of 
`broad' constructive mathematics.- Appendices.- Bibliography.

 SUPPLEMENT. N.A.Shanin. On operational approach to
explanation of the sense of sentences.

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