Recursively Enumerable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets

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Springer Science & Business Media, Nov 1, 1999 - Mathematics - 437 pages
2 Reviews
..."The book, written by one of the main researchers on the field, gives a complete account of the theory of r.e. degrees. .... The definitions, results and proofs are always clearly motivated and explained before the formal presentation; the proofs are described with remarkable clarity and conciseness. The book is highly recommended to everyone interested in logic. It also provides a useful background to computer scientists, in particular to theoretical computer scientists." Acta Scientiarum Mathematicarum, Ungarn 1988 ..."The main purpose of this book is to introduce the reader to the main results and to the intricacies of the current theory for the recurseively enumerable sets and degrees. The author has managed to give a coherent exposition of a rather complex and messy area of logic, and with this book degree-theory is far more accessible to students and logicians in other fields than it used to be." Zentralblatt für Mathematik, 623.1988
 

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Contents

III
7
IV
8
V
10
VI
11
VII
14
VIII
18
IX
24
X
27
LIII
195
LIV
199
LV
203
LVI
207
LVII
215
LVIII
224
LIX
230
LX
233

XI
32
XII
36
XIII
40
XIV
46
XV
52
XVI
56
XVII
60
XVIII
64
XIX
65
XX
69
XXI
75
XXII
77
XXIII
80
XXIV
84
XXV
87
XXVI
88
XXVII
92
XXVIII
93
XXIX
96
XXX
97
XXXI
100
XXXII
103
XXXIII
110
XXXIV
118
XXXV
121
XXXVI
127
XXXVII
129
XXXVIII
130
XXXIX
134
XL
137
XLI
142
XLII
147
XLIII
151
XLIV
152
XLV
157
XLVI
161
XLVII
168
XLVIII
174
XLIX
178
L
181
LI
187
LII
190
LXI
241
LXII
242
LXIII
246
LXIV
253
LXV
259
LXVI
270
LXVII
272
LXVIII
279
LXIX
281
LXX
282
LXXI
288
LXXII
294
LXXIII
296
LXXIV
300
LXXV
301
LXXVI
304
LXXVII
308
LXXVIII
309
LXXIX
315
LXXX
316
LXXXI
320
LXXXII
325
LXXXIII
327
LXXXIV
331
LXXXV
338
LXXXVI
341
LXXXVII
345
LXXXVIII
348
LXXXIX
354
XC
359
XCI
362
XCII
363
XCIII
365
XCIV
368
XCV
374
XCVI
379
XCVII
383
XCVIII
385
XCIX
389
C
419
CI
429
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Page x - The conclusion is unescapable that even for such a fixed, well defined body of mathematical propositions, mathematical thinking is, and must remain, essentially creative. To the writer's mind, this conclusion must inevitably result in at least a partial reversal of the entire axiomatic trend of the late nineteenth and early twentieth centuries, with a return to meaning and truth as being of the essence of mathematics.
Page 402 - Recursive functionals and quantifiers of finite types I, Trans. Amer. Math. Soc. 91 (1959), 1-52.
Page vii - Plans for books are discussed and argued about at length. Later, encouragement is given and revisions suggested. But it is the authors who do the work; if. as we hope, the series proves of value, the credit will be theirs. History of the fi-Group. During 1968 the idea of an integrated series of monographs on mathematical logic was first mooted. Various discussions led to a meeting at Oberwolfach in the spring of 1969. Here the founding members of the group (R.
Page viii - Bibliography, in an outstandingly generous way. We could always rely on their readiness to provide help wherever it was needed. Assistance in many various respects was provided by Drs. U. Feigner and K. Gloede (till 1975) and Drs. D. Schmidt and H. Zeitler (till 1979). Last but not least, our indefatigable secretary Elfriede Ihrig was and is essential in running our enterprise. We thank all those concerned. Heidelberg, September 1982 R.
Page vii - Logik" of the Heidelberger Akademie der Wissenschaften) On Perspectives. Mathematical logic arose from a concern with the nature and the limits of rational or mathematical thought, and from a desire to systematize the modes of its expression. The pioneering investigations were diverse and largely autonomous. As time passed, and more particularly in the last two decades, interconnections between different lines of research and links with other branches of mathematics proliferated. The subject is now...

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