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

Couverture
Springer Science & Business Media, 1 nov. 1999 - 437 pages
..."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
 

Table des matières

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

XII
32
XIII
36
XIV
40
XV
46
XVI
52
XVII
56
XVIII
60
XIX
64
XX
65
XXI
69
XXII
75
XXIII
77
XXIV
80
XXV
84
XXVI
87
XXVII
88
XXVIII
92
XXIX
93
XXX
96
XXXI
97
XXXII
100
XXXIII
103
XXXIV
110
XXXV
118
XXXVI
121
XXXVII
127
XXXIX
129
XL
130
XLI
134
XLII
137
XLIII
142
XLIV
147
XLV
151
XLVI
152
XLVII
157
XLVIII
161
XLIX
168
L
174
LI
178
LII
181
LIII
187
LIV
190
LXIII
241
LXIV
242
LXV
246
LXVI
253
LXVII
259
LXVIII
270
LXIX
272
LXX
279
LXXI
281
LXXII
282
LXXIII
288
LXXIV
294
LXXV
296
LXXVI
300
LXXVII
301
LXXVIII
304
LXXIX
308
LXXX
309
LXXXI
315
LXXXII
316
LXXXIII
320
LXXXIV
325
LXXXV
327
LXXXVI
331
LXXXVII
338
LXXXVIII
341
LXXXIX
345
XC
348
XCI
354
XCII
359
XCIII
362
XCIV
363
XCV
365
XCVI
368
XCVII
374
XCVIII
379
XCIX
383
C
385
CI
389
CII
419
CIII
429
Droits d'auteur

Autres éditions - Tout afficher

Expressions et termes fréquents

Fréquemment cités

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 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...

Informations bibliographiques