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Recursion Theory

About this Title

Anil Nerode and Richard A. Shore, Editors

Publication: Proceedings of Symposia in Pure Mathematics
Publication Year: 1985; Volume 42
ISBNs: 978-0-8218-1447-5 (print); 978-0-8218-9334-0 (online)
DOI: https://doi.org/10.1090/pspum/042

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Table of Contents

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Front/Back Matter

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I. Classical recursion theory

• Carl G. Jockusch, Jr. and Richard A. Shore – REA operators, r.e. degrees and minimal covers [MR 791048]
• Manuel Lerman – The embedding problem for the recursively enumerable degrees [MR 791049]
• Wolfgang Maass – Major subsets and automorphisms of recursively enumerable sets [MR 791050]
• Richard A. Shore – The structure of the degrees of unsolvability [MR 791051]
• Robert I. Soare – Tree arguments in recursion theory and the $0''’$-priority method [MR 791052]
• Michael Stob – Major subsets and the lattice of recursively enumerable sets [MR 791053]

II. Generalized recursion theory

• S. C. Kleene – Unimonotone functions of finite types (Recursive functionals and quantifiers of finite types revisited IV) [MR 791054]
• Phokion G. Kolaitis – Canonical forms and hierarchies in generalized recursion theory [MR 791055]
• Dag Normann – Aspects of the continuous functionals [MR 791056]
• Gerald E. Sacks – Post’s problem in $E$-recursion [MR 791057]
• Theodore A. Slaman – The $E$-recursively enumerable degrees are dense [MR 791058]

III. Fine structure and descriptive

• René David and Sy D. Friedman – Uncountable ZF-ordinals [MR 791059]
• Hans-Dieter Donder – Another look at gap-1 morasses [MR 791060]
• H.-D. Donder, R. B. Jensen and L. J. Stanley – Condensation-coherent global square systems [MR 791061]
• Sy D. Friedman – Fine structure theory and its applications [MR 791062]
• Alexander S. Kechris – Determinacy and the structure of $L(\mathbf {R})$ [MR 791063]
• Alain Louveau – Recursivity and capacity theory [MR 791064]
• Donald A. Martin – A purely inductive proof of Borel determinacy [MR 791065]

IV. Effective mathematics

• T. Millar – Decidable Ehrenfeucht theories [MR 791066]
• A. Nerode and J. Remmel – A survey of lattices of r.e. substructures [MR 791067]
• A. Seidenberg – Survey of constructions in Noetherian rings [MR 791068]

V. Foundations and complexity theory

• Jean-Yves Girard and Jean-Pierre Ressayre – Eléments de logique $\Pi ^1_n$ [MR 791069]
• Kenneth McAloon – Paris-Harrington incompleteness and progressions of theories [MR 791070]
• Stephen G. Simpson – Reverse mathematics [MR 791071]
• Robert M. Solovay – Infinite fixed-point algebras [MR 791072]
• S. S. Wainer – The “slow-growing” $\Pi ^1_2$ approach to hierarchies [MR 791073]
• Paul Young – Gödel theorems, exponential difficulty and undecidability of arithmetic theories: an exposition [MR 791074]