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 Algebra Logika, 2002, Volume 41, Number 5, Pages 515–530 (Mi al195)

Automorphism Groups of Computably Enumerable Predicates

E. Combarro

Abstract: We study automorphism groups of two important predicates in computability theory: the predicate $x\in W_y$ and the graph of a universal partially computable function. It is shown that all automorphisms of the predicates in question are computable. The actions of the automorphism groups on some index sets are examined, and we establish a number of results on the structure of these. We also look into homomorphisms of the two predicates. In this case the situation changes: all homomorphisms of the universal function are computable, but in each Turing degree, homomorphisms of $x\in W_y$ exist.

Keywords: automorphism group, homomorphism, computably enumerable predicate

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English version:
Algebra and Logic, 2002, 41:5, 285–294

Bibliographic databases:

UDC: 510.57

Citation: E. Combarro, “Automorphism Groups of Computably Enumerable Predicates”, Algebra Logika, 41:5 (2002), 515–530; Algebra and Logic, 41:5 (2002), 285–294

Citation in format AMSBIB
\Bibitem{Com02} \by E.~Combarro \paper Automorphism Groups of Computably Enumerable Predicates \jour Algebra Logika \yr 2002 \vol 41 \issue 5 \pages 515--530 \mathnet{http://mi.mathnet.ru/al195} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1953177} \zmath{https://zbmath.org/?q=an:1010.03031} \transl \jour Algebra and Logic \yr 2002 \vol 41 \issue 5 \pages 285--294 \crossref{https://doi.org/10.1023/A:1020975619422} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42249102789} 

• http://mi.mathnet.ru/eng/al195
• http://mi.mathnet.ru/eng/al/v41/i5/p515

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This publication is cited in the following articles:
1. Combarro E.F., “Symmetry of the universal computable function: A study of its automorphisms, homomorphisms and isomorphic embeddings”, Logic Colloquium '02, Lecture Notes in Logic, 27, 2006, 152–171
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