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We describe a variation of Ash’s η-system and give a new proof of Ash’s metatheorem. As an application, we prove a generalization of Ash and Knight’s theorem on pairs of structures.



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[1]Ash, C. J., Recursive labelling systems and stability of recursive structures in hyperarithmetical degrees. Transactions of the American Mathematical Society, vol. 298 (1986), no. 2, pp. 497514.
[2]Ash, C. J., Stability of recursive structures in arithmetical degrees. Annals of Pure and Applied Logic, vol. 32 (1986), no. 2, pp. 113135.
[3]Ash, C. J., Labelling systems and r.e. structures. Annals of Pure and Applied Logic, vol. 47 (1990), no. 2, pp. 99119.
[4]Ash, C. J. and Knight, J. F., Pairs of recursive structures. Annals of Pure and Applied Logic, vol. 46 (1990), no. 3, pp. 211234.
[5]Ash, C. J. and Knight, J. F., Mixed systems, this Journal, vol. 59 (1994), no. 4, pp. 13831399.
[6]Ash, C. J. and Knight, J. F., Ramified systems. Annals of Pure and Applied Logic, vol. 70 (1994), no. 3, pp. 205221.
[7]Ash, C. J. and Knight, J. F., Computable structures and the hyperarithmetical hierarchy, Studies in Logic and the Foundations of Mathematics, vol. 144, Elsevier, Amsterdam, 2000.
[8]Fokina, Ekaterina B. and Friedman, Sy-David, Equivalence relations on classes of computable structures. In Mathematical theory and computational practice, Lecture Notes in Computer Science, vol. 5635, Springer, Berlin, 2009, pp. 198207.
[9]Fokina, E. B., Friedman, S., Harizanov, V., Knight, J. F., McCoy, C., and Montalbán, A., Isomorphism and bi-embeddability relations on computable structures, this Journal, vol. 77 (2012), no. 1, pp. 122132.
[10]Friedman, Harvey and Stanley, Lee, A Borel reducibility theory for classes of countable structures, this Journal, vol. 54 (1989), no. 3, pp. 894914.
[11]Harrington, L., Mclaughlin’s conjecture. Handrwitten notes, 11 pages, September 76.
[12]Harrington, L., N, building nonstandard models of peano arithmetic, Handrwitten notes, 1979.
[13]Harris, Kenneth and Montalbán, A., Boolean algebra approximations, Transactions of the Amertical Mathematical Society. to appear.
[14]Knight, J. F., A metatheorem for constructions by finitely many workers, this Journal, vol. 55 (1990), no. 2, pp. 787804.
[15]Knight, J. F., Constructions by transfinitely many workers. Annals of Pure and Applied Logic, vol. 48 (1990), no. 3, pp. 237259.
[16]Knight, J. F., Requirement systems, this Journal, vol. 60 (1995), no. 1, pp. 222245.
[17]Lachlan, A. H., The priority method for the construction of recursively enumerable sets. In Cambridge Summer School in Mathematical Logic (Cambridge, 1971), Lecture Notes in Mathematics, vol. 337, Springer, Berlin, 1973, pp. 299310.
[18]Lerman, Manuel, A framework for priority arguments, Lecture Notes in Logic. vol. 34, Association for Symbolic Logic, La Jolla, CA, 2010.
[19]Lempp, Steffen and Lerman, Manuel, Priority arguments using iterated trees of strategies. In Recursion theory week (Oberwolfach, 1989), Lecture Notes in Mathematics, vol. 1432, Springer, Berlin, 1990, pp. 277296.
[20]Lempp, Steffen and Lerman, Manuel, A general framework for priority arguments. Bulletin of Symbolic Logic, vol. 1 (1995), no. 2, pp. 189201.
[21]Marcone, Alberto and Montalbán, A., The Veblen functions for computability theorists, this Journal, vol. 76 (2011), no. 2, pp. 575602.
[22]Montalbán, Antonio, Classes of structures with no intermediate isomorphism problems. in preparation.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
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