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Definability in the language of functional equations of a countable-valued logic
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S. S. Marchenkov
Published/Copyright:
May 1, 2014
Abstract
The paper is concerned with definability of functions and relations in the FE language of functional equations of a countable-valued logic. The class of relations definable by functional equations over the set of functions {0, x + 1} is shown to coincide with the class ∑11 of the analytical Kleene hierarchy. Two extensions of the FE language are proposed that are equivalent in their expressibility to the FE language with functional constants for all homogeneous functions.
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 13-01-00958).
Published Online: 2014-5-1
Published in Print: 2013-12-1
© 2014 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Front matter
- Criterion for propositional calculi to be finitely generated
- Fast Catalan constant computation via the approximations obtained by the Kummer’s type transformations
- Cycle indices of an automaton
- Definability in the language of functional equations of a countable-valued logic
- On bigram languages
- The diagnosis of states of contacts
- Finite systems of generators of infinite subgroups of the Golod group
- On the number of cyclic points of random A-mapping
Articles in the same Issue
- Front matter
- Criterion for propositional calculi to be finitely generated
- Fast Catalan constant computation via the approximations obtained by the Kummer’s type transformations
- Cycle indices of an automaton
- Definability in the language of functional equations of a countable-valued logic
- On bigram languages
- The diagnosis of states of contacts
- Finite systems of generators of infinite subgroups of the Golod group
- On the number of cyclic points of random A-mapping
