R. Downey, D. Hirschfeldt, B. Khoussainov, “Uniformity in Computable Structure Theory”, Algebra Logika, 42:5 (2003), 566–593; Algebra and Logic, 42:5 (2003), 318

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Algebra i logika, 2003, Volume 42, Number 5, Pages 566–593 (Mi al44)

This article is cited in 23 scientific papers (total in 23 papers)

Uniformity in Computable Structure Theory

R. Downey^a, D. Hirschfeldt^b, B. Khoussainov^c

^a Victoria University of Wellington, School of Mathematics, Statistics and Computer Science
^b University of Chicago
^c University of Auckland

Full-text PDF (294 kB) Citations (23)

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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.

Keywords: computably categorical structure, intrinsically computable relation on a computable structure, relative computable structure, general computable structure.

Received: 10.11.2000

English version:
Algebra and Logic, 2003, Volume 42, Issue 5, Pages 318–332
DOI: https://doi.org/10.1023/A:1025971406116

Bibliographic databases:

UDC: 510.53

Language: Russian

Citation: R. Downey, D. Hirschfeldt, B. Khoussainov, “Uniformity in Computable Structure Theory”, Algebra Logika, 42:5 (2003), 566–593; Algebra and Logic, 42:5 (2003), 318–332

Citation in format AMSBIB

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\jour Algebra and Logic

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\crossref{https://doi.org/10.1023/A:1025971406116}

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Linking options:

https://www.mathnet.ru/eng/al44

https://www.mathnet.ru/eng/al/v42/i5/p566

This publication is cited in the following 23 articles:

Nadim Kasymov, Nadira Karimova, Bakh Khoussainov, Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science, 2024, 1
Andrey Frolov, Maxim Zubkov, “On categoricity of scattered linear orders of constructive ranks”, Arch. Math. Logic, 2024
WESLEY CALVERT, JOHANNA N. Y. FRANKLIN, DAN TURETSKY, “STRUCTURAL HIGHNESS NOTIONS”, J. symb. log., 88:4 (2023), 1692
Antonio Montalbán, Computable Structure Theory, 2021
Downey R., Greenberg N., Melnikov A., Ng K.M., Turetsky D., “Punctual Categoricity and Universality”, J. Symb. Log., 85:4 (2020), 1427–1466
S. S. Goncharov, V. Harizanov, R. Miller, “On Decidable Categoricity and Almost Prime Models”, Sib. Adv. Math., 30:3 (2020), 200
Bazhenov N. Downey R. Kalimullin I. Melnikov A., “Foundations of Online Structure Theory”, Bull. Symb. Log., 25:2 (2019), 141–181
Melnikov A.G., “Torsion-Free Abelian Groups With Optimal Scott Families”, J. Math. Log., 18:1 (2018)
Korovina M. Kudinov O., “Complexity For Partial Computable Functions Over Computable Polish Spaces”, Math. Struct. Comput. Sci., 28:3, SI (2018), 429–447
Greenberg N., Melnikov A.G., Knight J.F., Turetsky D., “Uniform Procedures in Uncountable Structures”, J. Symb. Log., 83:2 (2018), 529–550
Korovina M. Kudinov O., “Computable Elements and Functions in Effectively Enumerable Topological Spaces”, Math. Struct. Comput. Sci., 27:8 (2017), 1466–1494
Montalban A., “Effectively Existentially-Atomic Structures”, Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60Th Birthday, Lecture Notes in Computer Science, 10010, eds. Day A., Fellows M., Greenberg N., Khoussainov B., Melnikov A., Rosamond F., Springer International Publishing Ag, 2017, 221–237
Miller R., “Revisiting Uniform Computable Categoricity: For the Sixtieth Birthday of Prof. Rod Downey”, Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60Th Birthday, Lecture Notes in Computer Science, 10010, eds. Day A., Fellows M., Greenberg N., Khoussainov B., Melnikov A., Rosamond F., Springer International Publishing Ag, 2017, 254–270
Hirschfeldt D.R. Kramer K. Miller R. Shlapentokh A., “Categoricity Properties For Computable Algebraic Fields”, Trans. Am. Math. Soc., 367:6 (2015), PII S0002-9947(2014)06094-7, 3981–4017
Astor E.P., “Asymptotic Density, Immunity and Randomness”, Computability, 4:2 (2015), 141–158
Montalban A., “a Robuster Scott Rank”, Proc. Amer. Math. Soc., 143:12 (2015), 5427–5436
Downey R.G., Kach A.M., Lempp S., Lewis-Pye A.E.M., Montalban A., Turetsky D.D., “the Complexity of Computable Categoricity”, Adv. Math., 268 (2015), 423–466
Barbara F. Csima, Valentina S. Harizanov, Russell Miller, Antonio Montalbán, “Computability of Fraïssé limits”, J. symb. log., 76:1 (2011), 66
Miller R., “D-Computable Categoricity for Algebraic Fields”, Journal of Symbolic Logic, 74:4 (2009), 1325–1351
Douglas Cenzer, Valentina Harizanov, David Marker, Carol Wood, “Preface”, Arch. Math. Logic, 48:1 (2009), 1

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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