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Book Review
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Book Information
Author(s):
M. C. Fitting
Title:
Fundamentals of generalized recursion theory
Additional book information:
Studies in Logic and The Foundations of Mathematics, Volume 105, North-Holland Publishing Company, Amsterdam, 1981, xx + 302 pp., $63.75 U.S./Dfl. 150.00
References:
- [ABH] S. I. Adian, W. W. Boone and G. Higman (eds.), Word problems II, North-Holland, 1980. MR 579933
- [B] A. Baker, Recent advances in transcendence theory, Trudy Math. Inst. Steklov 132 (1973), 67-69. MR 332669
- [BD] A. Baker and H. Davenport, The equations 3x³ - 2 = y² and 8x² - 7 = z², Quarterly J. Math. Oxford Ser. (2) 20 (1969), 129-137. MR 248079
- [B1] J. Barwise (ed.), Syntax and semantics of infinitary languages, Lecture Notes, vol. 72, Springer-Verlag, 1968. MR 234827
- [B2] J. Barwise (ed.), Handbook of mathematical logic, North-Hollaǹd, 1977. MR 457132
- [Bi] E. Bishop, Foundations of constructive analysis, McGraw-Hill, 1967. MR 221878
- [BV] E. Bombieri and J. Vaalen, On Siegel's Lemma, Invent. Math. 73 (1983), 11-32, addendum 75 (1984), 377. MR 707346
- [Ca] G. Cantor, Gesammelte Abhandlungen (E. Zermelo, ed.), Springer-Verlag, 1932. MR 148517
- [C1] J. W. S. Cassels, Diophantine equations with special reference to elliptic curves, J. London Math. Soc. 41 (1966), 193-291. MR 199150
- [C2] J. W. S. Cassels, Review of: Introduction to Number Theory by Hua Loo Keng (translated by Peter Shiu), Math. Intelligencer 5 no 2 (1983), 57.
- [DLS] D. van Dalen, D. Lascar and T. J. Smiley (eds.), Logic Colloquium '80, North-Holland, 1983. MR 673782
- [E] J. L. Ersov, Theorie der Numerierungen II, III, Z. Math. Logik Grundlag. Math. 21 (1975) 473-584; und 23 (1977), 289-371. MR 389562
- [GY] R. O. Gandy and C. E. M. Yates (eds.), Logic Colloquium '69, North-Holland, 1971. MR 272598
- [G1] K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Mh. Math. Physik 38 (1931), 173-198. MR 1549910
- [G2] K. Gödel, The consistency of the continuum hypothesis, Ann. Math. Studies no. 3, 1940. MR 2514
- [H] G. Higman, Subgroups of finitely presented groups, Proc. Roy. Soc. Ser. A 262 (1961), 455-475. MR 130286
- [HB] D. Hilbert and P. Bernays, Grundlagen der Mathematik, vol. 2, Springer-Verlag, Berlin and New York, 1970. MR 272596
- [HS] L. Harrington and S. Shelah, The undecidability of the recursively enumerable degrees, Bull. Amer. Math. Soc. (N.S). 6 (1982), 79-80. MR 634436
- [J] R. B. Jensen, The fine structure of the constructible hierarchy, Ann. of Math. Logic 4 (1972), 229-308. MR 309729
- [K1] S. C. Kleene, Hierarchies of number-theoretic predicates, Bull. Amer. Math. Soc. 61 (1955), 193-213; reviewed MR 17 (1956), 4. MR 70593
- [K2] S. C. Kleene, Recursive functional and quantifiers of finite type, Trans. Amer. Math. Soc. 91 (1959), 1-52. MR 102480
- [Kn] W. Knorr, La croix des mathématiciens, Bull. Amer. Math. Soc. (N.S.) 9 (1983), 41-69. MR 699316
- [Kr] G. Kreisel, Mathematical logic: tool and object lesson for science, Synthese 62 (1985), 139-152. MR 788502
- [LM] G. Longo and E. Moggi, The hereditary partial effective functional and recursion theory in higher types, J. Symbolic Logic 49 (1984), 1319-1332. MR 771797
- [M] D. A. Martin, Borel determinacy, Ann. of Math. (2) 102 (1975), 363-371. MR 403976
- [PR] M. B. Pour-El and I. Richards, The wave equation with computable initial data such that its unique solution is not computable, Advances in Math. 39 (1981), 215-239; reviewed J. Symbolic Logic 47 (1982), 900-902. MR 614161
- [S] T. L. Saaty (ed.), Lectures on modern mathematics. III, Wiley, New York, 1965. MR 177844
- [Sh] J. R. Shoenfield, Degrees of undecidability, North-Holland, 1971. MR 282830
- [Sho] R. A. Shore, The theory of the degrees below 0', J. London Math. Soc. (2) 24 (1981), 1-14. MR 623666
- [Si] W. Sierpiński, Le dernier théorème de Fermat pour les nombres ordinaux, Fund. Math. 37 (1950), 201-205. MR 40372
- [Sm] S. Smale, The fundamental theorem of algebra and complexity theory, Bull. Amer. Math. Soc. (N.S.) 4 (1981), 1-36. MR 590817
- [Y] C. E. M. Yates, Prioric games and minimal degrees below 0', Fund. Math. 82 (1974), 217-237. MR 406784
- [Z] K. Zuse, Der Computer―mein Lebenswerk, Verlag für moderne Industrie, Munich, 1970.
Additional Information:
Reviewer(s):
G.
Kreisel
Review Information:
Journal:
Bull. Amer. Math. Soc.
13
(1985),
182-197.
DOI:
10.1090/S0273-0979-1985-15413-8
PII:
S 0273-0979(1985)15413-8
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