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Petersburg Department of Steklov Institute of Mathematics

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PREPRINT 06/2000

ξ. α. ϋΑΞΙΞ
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όσλιϊ ζιξιταςξοηο χαςιαξτα νατενατιώεσλοηο αξαμιϊα

This preprint was accepted ιΐΞΨ 2000

Contact:
` ξ.α.ϋΑΞΙΞ `

ABSTRACT:
N.A.Shanin. A sketch of a finitary version of mathematical
analysis.
CONTENTS.1. On basic ideas of finitary mathematics.- 2.
Particular
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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