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Handbook of computability theory. (English) Zbl 0923.03001

Studies in Logic and the Foundations of Mathematics. 140. Amsterdam: Elsevier. xii, 727 p. Dfl. 149.50; EUR 133.87; $ 149.00 (1999).

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[The articles of this volume will be reviewed individually.]
The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little to the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.
Indexed articles:
Soare, Robert I., The history and concept of computability, 3-36 [Zbl 0948.03038]
Cenzer, Douglas, \(\Pi_1^0\) classes in computability theory, 37-85 [Zbl 0939.03047]
Odifreddi, Piergiorgio, Reducibilities, 89-119 [Zbl 0945.03065]
Cooper, S. Barry, Local degree theory, 121-153 [Zbl 0944.03035]
Slaman, Theodore A., The global structure of the Turing degrees, 155-168 [Zbl 0944.03034]
Shore, Richard A., The recursively enumerable degrees, 169-197 [Zbl 0947.03061]
Soare, Robert I., An overview of the computably enumerable sets, 199-248 [Zbl 0939.03045]
Normann, Dag, The continuous functionals, 251-275 [Zbl 0965.03058]
Chong, C. T.; Friedman, S. D., Ordinal recursion theory, 277-299 [Zbl 0947.03063]
Sacks, Gerald E., \(E\)-recursion, 301-314 [Zbl 0947.03064]
Hinman, Peter G., Recursion on abstract structures, 315-359 [Zbl 0946.03054]
Stoltenberg-Hansen, V.; Tucker, J. V., Computable rings and fields, 363-447 [Zbl 0944.03040]
Pour-El, Marian Boykan, The structure of computability in analysis and physical theory: An extension of Church’s thesis, 449-471 [Zbl 0945.03091]
Ershov, Yuri L., Theory of numberings, 473-503 [Zbl 0948.03040]
Millar, Terrence S., Pure recursive model theory, 507-532 [Zbl 0940.03046]
Schwichtenberg, Helmut, Classifying recursive functions, 533-586 [Zbl 0978.03035]
Clote, P., Computation models and function algebras, 589-681 [Zbl 0942.68049]
Ambos-Spies, Klaus, Polynomial time reducibilities and degrees, 683-705 [Zbl 0941.03043]

MSC:

03-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mathematical logic and foundations
00B15 Collections of articles of miscellaneous specific interest
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