Abstract
We introduce the notions of a complete set of computably infinitary \(\Pi^0_n\) relations on a structure, of the jump of a structure, and of admitting n th jump inversion.
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References
Ash, C.J., Knight, J.: Computable Structures and the Hyperarithmetical Hierarchy. Elsevier Science, Amsterdam (2000)
Ash, C., Knight, J., Manasse, M., Slaman, T.: Generic copies of countable structures. Ann. Pure Appl. Logic 42(3), 195–205 (1989)
Ash, C.J.: A construction for recursive linear orderings. J. Symbolic Logic 56(2), 673–683 (1991)
Chisholm, J., Fokina, E., Goncharov, S., Knight, J., Miller, S.: Intrinsic bounds on complexity at limit levels. Journal of Symbolic Logic (to appear)
Chisholm, J.: Effective model theory vs. recursive model theory. J. Symbolic Logic 55(3), 1168–1191 (1990)
Downey, R., Jockusch, C.G.: Every low Boolean algebra is isomorphic to a recursive one. Proc. Amer. Math. Soc. 122(3), 871–880 (1994)
Downey, R., Knight, J.F.: Orderings with αth jump degree \({\bf 0}\sp {(\alpha)}\). Proc. Amer. Math. Soc. 114(2), 545–552 (1992)
Goncharov, S., Harizanov, V., Knight, J., McCoy, C., Miller, R., Solomon, R.: Enumerations in computable structure theory. Ann. Pure Appl. Logic 136(3), 219–246 (2005)
Harris, K., Montalbán, A.: On the n-back-and-forth types of Boolean algebras (submitted for publication)
Kach, A., Montalbán, A.: Linear orders with finitely many descending cuts (in preparation)
Knight, J.F., Stob, M.: Computable Boolean algebras. J. Symbolic Logic 65(4), 1605–1623 (2000)
Thurber, J.J.: Every \({\rm low}\sb 2\) Boolean algebra has a recursive copy. Proc. Amer. Math. Soc. 123(12), 3859–3866 (1995)
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Montalbán, A. (2009). Notes on the Jump of a Structure. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds) Mathematical Theory and Computational Practice. CiE 2009. Lecture Notes in Computer Science, vol 5635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03073-4_38
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DOI: https://doi.org/10.1007/978-3-642-03073-4_38
Publisher Name: Springer, Berlin, Heidelberg
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