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  1. Computability and continuity in metric partial algebras equipped with computability structures.Fredrik Dahlgren - 2004 - Mathematical Logic Quarterly 50 (4-5):486-500.
    In this paper we give an axiomatisation of the concept of a computability structure with partial sequences on a many‐sorted metric partial algebra, thus extending the axiomatisation given by Pour‐El and Richards in [9] for Banach spaces. We show that every Banach‐Mazur computable partial function from an effectively separable computable metric partial Σ‐algebraAto a computable metric partial Σ‐algebraBmust be continuous, and conversely, that every effectively continuous partial function with semidecidable domain and which preserves the computability of a computably enumerable dense (...)
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  • Partial Horn logic and cartesian categories.Erik Palmgren & Steven J. Vickers - 2007 - Annals of Pure and Applied Logic 145 (3):314-353.
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  • Computability and continuity in computable metric partial algebras equipped with computability structures.Fredrik Dahlgren - 2004 - Mathematical Logic Quarterly 50 (4):486.
    In this paper we give an axiomatisation of the concept of a computability structure with partial sequences on a many-sorted metric partial algebra, thus extending the axiomatisation given by Pour-El and Richards in [9] for Banach spaces. We show that every Banach-Mazur computable partial function from an effectively separable computable metric partial Σ-algebra A to a computable metric partial Σ-algebra B must be continuous, and conversely, that every effectively continuous partial function with semidecidable domain and which preserves the computability of (...)
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  • Stability of representations of effective partial algebras.Jens Blanck, Viggo Stoltenberg-Hansen & John V. Tucker - 2011 - Mathematical Logic Quarterly 57 (2):217-231.
    An algebra is effective if its operations are computable under some numbering. When are two numberings of an effective partial algebra equivalent? For example, the computable real numbers form an effective field and two effective numberings of the field of computable reals are equivalent if the limit operator is assumed to be computable in the numberings . To answer the question for effective algebras in general, we give a general method based on an algebraic analysis of approximations by elements of (...)
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