Abstract
The complexity of priority proofs in recursion theory has been growing since the first priority proofs in [1] and [7]. Refined versions of classic priority proofs can be found in [11]. To this date, this part of recursion theory is at about the same stage of development as real analysis was in the early days, when the notions of topology, continuity, compactness, vector space, inner product space, etc., were not invented. There were no general theorems involving these concepts to prove results about the real numbers and the proofs were repetitive and lengthy.
The author wishes to thank Anil Nerode and the organizing committee who made the presentation and publication of this paper possible.
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References
Friedberg, R. [1957], Two recursively enumerable sets of incomparable degrees of unsolvability. Proc. Nat. Acad. Sciences, USA 43, 236–238.
Groszek, M. and T. Slaman [1987], Foundations of the priority method I, Finite and Infinite Injury (preprint).
Kirby, L. and J. Paris [1978], Σ Collection schemas in Arithmetic. Logic Colloquium 77, North-Holland, Amsterdam, 199–209.
Kontostathis, K. [1988], On the Construction of Degrees of Unsolvability. Ph.D. Thesis, Duke University, 1–44.
Kontostathis, K. [1991], Topological Framework for Non-priority. Zeits. f. Math. Logik, u. Grundl. der Math. 37, 495–500.
Lempp, S. and M. Lerman [1990], Priority Arguments Using Iterated Trees of Strategies. Lecture Notes in Mathematics 1432, Springer-Verlag.
Muchnick, A. [1956], On the unsolvability of the problem of reducibility in the theory of algorithms. Dokl. Akad. SSSR 108, 194–197.
Nerode, A., A. Yakhnis and V. Yakhnis [1990], Concurrent Programs as Strategies in Games. MSI Technical Report, Cornell University.
Shoenfield, J. [1967], Mathematical Logic. Addison-Wesley.
Slaman, T. and W. Woodin [1989], Collection and the Finite Injury Method. Mathematical Logic and its Applications, Lecture Notes in Mathematics 1388, Springer-Verlag.
Soare, R. [1987], Recursively Enumerable Sets and Degrees. Springer-Verlag.
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Kontostathis, K. (1993). The Combinatorics of the Friedberg-Muchnick Theorem. In: Crossley, J.N., Remmel, J.B., Shore, R.A., Sweedler, M.E. (eds) Logical Methods. Progress in Computer Science and Applied Logic, vol 12. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0325-4_15
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