Geodesic
Computable categoricity versus relative computable categoricity
Rodney G. Downey 1   ; Asher M. Kach 2   ; Steffen Lempp 3   ; Daniel D. Turetsky 4
1 Department of Mathematics Victoria University of Wellington Wellington, New Zealand
2 Department of Mathematics University of Chicago 5734 S. University Ave. Chicago, IL 60637, U.S.A.
3 Department of Mathematics University of Wisconsin Madison, WI 53706-1388, U.S.A.
4 Kurt Gödel Research Center for Mathematical Logic Währinger Straße 25 1090 Wien, Austria
Fundamenta Mathematicae, Tome 221 (2013) no. 2, pp. 129-159 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the notion of computable categoricity of computable structures, comparing it especially to the notion of relative computable categoricity and its relativizations. We show that every 1 decidable computably categorical structure is relatively $\Delta ^0_2$ categorical. We study the complexity of various index sets associated with computable categoricity and relative computable categoricity. We also introduce and study a variation of relative computable categoricity, comparing it to both computable categoricity and relative computable categoricity and its relativizations.
DOI : 10.4064/fm221-2-2
Keywords: study notion computable categoricity computable structures comparing especially notion relative computable categoricity its relativizations every nbsp decidable computably categorical structure relatively delta nbsp categorical study complexity various index sets associated computable categoricity relative computable categoricity introduce study variation relative computable categoricity comparing computable categoricity relative computable categoricity its relativizations

Rodney G. Downey  1   ; Asher M. Kach  2   ; Steffen Lempp  3   ; Daniel D. Turetsky  4

1 Department of Mathematics Victoria University of Wellington Wellington, New Zealand
2 Department of Mathematics University of Chicago 5734 S. University Ave. Chicago, IL 60637, U.S.A.
3 Department of Mathematics University of Wisconsin Madison, WI 53706-1388, U.S.A.
4 Kurt Gödel Research Center for Mathematical Logic Währinger Straße 25 1090 Wien, Austria 
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     author = {Rodney G. Downey and Asher M. Kach and Steffen Lempp and Daniel D. Turetsky},
     title = {Computable categoricity
 versus relative computable categoricity},
     journal = {Fundamenta Mathematicae},
     pages = {129--159},
     year = {2013},
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     number = {2},
     doi = {10.4064/fm221-2-2},
     language = {en},
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 versus relative computable categoricity
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Rodney G. Downey; Asher M. Kach; Steffen Lempp; Daniel D. Turetsky. Computable categoricity
 versus relative computable categoricity. Fundamenta Mathematicae, Tome 221 (2013) no. 2, pp. 129-159. doi: 10.4064/fm221-2-2

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