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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.

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[1] Brattka V. and Presser G., Computability on subsets of metric spaces . Theoretical Computer Science, vol. 305 (2003), pp. 4376.
[2] Brattka V. and Weihrauch K., Computability on subsets of euclidean space i: Closed and compact subsets . Theoretical Computer Science, vol. 219 (1999), pp. 6593.
[3] Hertling P., Effectivity and effective continuity of functions between computable metric spaces , Combinatorics, Complexity and Logic, Proceedings of DMTCS96 (Bridges D. S. et al., editors), Springer, Berlin, 1996, pp. 264275.
[4] Iljazović Z., Isometries and computability structures . Journal of Universal Computer Science, vol. 16 (2010), no. 18, pp. 25692596.
[5] Melnikov A. G., Computably isometric spaces . The Journal of Symbolic Logic, vol. 78 (2013), pp. 10551085.
[6] Mori T., Tsujji Y., and Yasugi M., Computability structures on metric spaces , Combinatorics, Complexity and Logic, Proceedings of DMTCS96 (Bridges D. S. et al., editors), Springer, Berlin, 1996, pp. 351362.
[7] Pour-El M. B. and Richards J. I., Computability in Analysis and Physics, Springer, Berlin, 1989.
[8] Turing A. M., On computable numbers, with an application to the entscheidungsproblem . Proceedings of the London Mathematical Society, vol. 42 (1936), pp. 230265.
[9] Weihrauch K., Computability on computable metric spaces . Theoretical Computer Science, vol. 113 (1993), pp. 191210.
[10] Weihrauch K., Computable Analysis, Springer, Berlin, 2000.
[11] Yasugi M., Mori T., and Tsujji Y., Effective properties of sets and functions in metric spaces with computability structure . Theoretical Computer Science, vol. 66 (1999), pp. 127138.
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Bulletin of Symbolic Logic
  • ISSN: 1079-8986
  • EISSN: 1943-5894
  • URL: /core/journals/bulletin-of-symbolic-logic
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