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  1. Dieter Spreen (2014). An Isomorphism Theorem for Partial Numberings. In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter. 341-382.
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  2. Dieter Spreen (2014). Partial Numberings and Precompleteness. In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter. 325-340.
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  3. Dieter Spreen (2014). The Life and Work of Victor L. Selivanov. In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter. 1-8.
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  4. Dieter Spreen, Hannes Diener & Vasco Brattka, Logic, Computation, Hierarchies.
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  5. Ulrich Berger, Vasco Brattka, Andrei S. Morozov & Dieter Spreen (2012). Foreword. Annals of Pure and Applied Logic 163 (8):973-974.
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  6. Dieter Spreen (2010). Effectivity and Effective Continuity of Multifunctions. 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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  7. Serikzhan Badaev & Dieter Spreen (2005). A Note on Partial Numberings. 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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  8. Dieter Spreen (2005). Strong Reducibility of Partial Numberings. 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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  9. Dieter Spreen (2001). Can Partial Indexings Be Totalized? 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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  10. Dieter Spreen (2000). Corrigendum: On Effective Topological Spaces. Journal of Symbolic Logic 65 (4):1917-1918.
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  11. Dieter Spreen (1998). On Effective Topological Spaces. 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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  12. Dieter Spreen (1996). Effective Inseparability in a Topological Setting. 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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