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MAXIMAL COMPUTABILITY STRUCTURES

Published online by Cambridge University Press:  30 December 2016

ZVONKO ILJAZOVIĆ  and
LUCIJA VALIDŽIĆ
ZVONKO ILJAZOVIĆ
Affiliation:
DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE UNIVERSITY OF ZAGREB 10000 ZAGREB, CROATIA E-mail: zilj@math.hr
LUCIJA VALIDŽIĆ
Affiliation:
DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE UNIVERSITY OF ZAGREB 10000 ZAGREB, CROATIA E-mail: lvalidz@student.math.hr
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Abstract

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A computability structure on a metric space is a set of sequences which satisfy certain conditions. Of a particular interest are those computability structures which contain a dense sequence, so called separable computability structures. In this paper we observe maximal computability structures which are more general than separable computability structures and we examine their properties. In particular, we examine maximal computability structures on subspaces of Euclidean space, we give their characterization and we investigate conditions under which a maximal computability structure on such a space is unique. We also give a characterization of separable computability structures on a segment.

Keywords

03D9968Q99computable metric spaceseparable computability structuremaximal computability structure

Information

Type
Articles
Information
Bulletin of Symbolic Logic , Volume 22 , Issue 4 , December 2016 , pp. 445 - 468
Copyright
Copyright © The Association for Symbolic Logic 2016 

References

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