Uniformity in Computable Structure Theory |
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| Authors: | R. G. Downey D. R. Hirschfeldt B. Khoussainov |
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| Affiliation: | (1) School of Mathematical and Computing Sciences, Victoria University, Wellington, New Zealand;(2) Department of Mathematics, University of Chicago, USA;(3) Department of Computer Science, University of Auckland, Auckland, New Zealand |
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| Abstract: | We investigate the effects of adding uniformity requirements to concepts in computable structure theory such as computable categoricity (of a structure) and intrinsic computability (of a relation on a computable structure). We consider and compare two different notions of uniformity, previously studied by Kudinov and by Ventsov. We discuss some of their results and establish new ones, while also exploring the connections with the relative computable structure theory of Ash, Knight, Manasse, and Slaman and Chisholm and with previous work of Ash, Knight, and Slaman on uniformity in a general computable structure-theoretical setting. |
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| Keywords: | computably categorical structure intrinsically computable relation on a computable structure relative computable structure general computable structure |
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