13 found
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  1. On effective topological spaces.Dieter Spreen - 1998 - Journal of Symbolic Logic 63 (1):185-221.
    Starting with D. Scott's work on the mathematical foundations of programming language semantics, interest in topology has grown up in theoretical computer science, under the slogan `open sets are semidecidable properties'. But whereas on effectively given Scott domains all such properties are also open, this is no longer true in general. In this paper a characterization of effectively given topological spaces is presented that says which semidecidable sets are open. This result has important consequences. Not only follows the classical Rice-Shapiro (...)
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  2.  29
    Effective inseparability in a topological setting.Dieter Spreen - 1996 - Annals of Pure and Applied Logic 80 (3):257-275.
    Effective inseparability of pairs of sets is an important notion in logic and computer science. We study the effective inseparability of sets which appear as index sets of subsets of an effectively given topological T0-space and discuss its consequences. It is shown that for two disjoint subsets X and Y of the space one can effectively find a witness that the index set of X cannot be separated from the index set of Y by a recursively enumerable set, if X (...)
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  3. Can partial indexings be totalized?Dieter Spreen - 2001 - Journal of Symbolic Logic 66 (3):1157-1185.
    In examples like the total recursive functions or the computable real numbers the canonical indexings are only partial maps. It is even impossible in these cases to find an equivalent total numbering. We consider effectively given topological T 0 -spaces and study the problem in which cases the canonical numberings of such spaces can be totalized, i.e., have an equivalent total indexing. Moreover, we show under very natural assumptions that such spaces can effectively and effectively homeomorphically be embedded into a (...)
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  4.  41
    A note on partial numberings.Serikzhan Badaev & Dieter Spreen - 2005 - Mathematical Logic Quarterly 51 (2):129-136.
    The different behaviour of total and partial numberings with respect to the reducibility preorder is investigated. Partial numberings appear quite naturally in computability studies for topological spaces. The degrees of partial numberings form a distributive lattice which in the case of an infinite numbered set is neither complete nor contains a least element. Friedberg numberings are no longer minimal in this situation. Indeed, there is an infinite descending chain of non-equivalent Friedberg numberings below every given numbering, as well as an (...)
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  5.  21
    Foreword.Ulrich Berger, Vasco Brattka, Andrei S. Morozov & Dieter Spreen - 2012 - Annals of Pure and Applied Logic 163 (8):973-974.
  6.  11
    An isomorphism theorem for partial numberings.Dieter Spreen - 2014 - In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter. pp. 341-382.
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  7.  48
    Corrigendum: On effective topological spaces.Dieter Spreen - 2000 - Journal of Symbolic Logic 65 (4):1917-1918.
  8.  59
    Effectivity and effective continuity of multifunctions.Dieter Spreen - 2010 - Journal of Symbolic Logic 75 (2):602-640.
    If one wants to compute with infinite objects like real numbers or data streams, continuity is a necessary requirement: better and better (finite) approximations of the input are transformed into better and better (finite) approximations of the output. In case the objects are constructively generated, they can be represented by a finite description of the generating procedure. By effectively transforming such descriptions for the generation of the input (respectively, their codes) into (the code of) a description for the generation of (...)
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  9.  14
    Index.Dieter Spreen, Hannes Diener & Vasco Brattka - 2014 - In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter. pp. 411-414.
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  10.  23
    Logic, Computation, Hierarchies.Dieter Spreen, Hannes Diener & Vasco Brattka (eds.) - 2014 - De Gruyter.
    Published in honor of Victor L. Selivanov, the 17 articles collected in this volume inform on the latest developments in computability theory and its applications in computable analysis; descriptive set theory and topology; and the theory of omega-languages; as well as non-classical logics, such as temporal logic and paraconsistent logic. This volume will be of interest to mathematicians and logicians, as well as theoretical computer scientists.
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  11.  17
    Partial numberings and precompleteness.Dieter Spreen - 2014 - In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter. pp. 325-340.
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  12.  63
    Strong reducibility of partial numberings.Dieter Spreen - 2005 - Archive for Mathematical Logic 44 (2):209-217.
    A strong reducibility relation between partial numberings is introduced which is such that the reduction function transfers exactly the numbers which are indices under the numbering to be reduced into corresponding indices of the other numbering. The degrees of partial numberings of a given set with respect to this relation form an upper semilattice.In addition, Ershov’s completion construction for total numberings is extended to the partial case: every partially numbered set can be embedded in a set which results from the (...)
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  13.  16
    The life and work of Victor L. Selivanov.Dieter Spreen - 2014 - In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter. pp. 1-8.
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