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On the quantifier of limiting realizability

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Abstract

In the searches for“contentwise”-interesting constructive analogs of the theorems of classical mathematics, there occur useful logical connectives occupying an intermediate position between\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{\exists } \) and ∃ and between

and\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{v} \) denotes

denotes

Two logical connectives of this types, suggested by the theory of limitedly computable (semicomputable) functions and defined in terms of the basic logical connectives of constructive logic, viz., the quantifier\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\rightarrow}$}}{\exists } \) of limiting realizability and the quantifier\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\rightarrow}$}}{v} \) of limiting disjunction, are introduced into consideration in the article. A number of properties are established for these logical connectives.

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Authors
  1. N. A. Shanin
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 60, pp. 209–220, 1976. The basic content of the article was announced February 6, 1975.

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Shanin, N.A. On the quantifier of limiting realizability. J Math Sci 14, 1565–1572 (1980). https://doi.org/10.1007/BF01693989

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