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Book Review
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Book Information
Author(s):
Christian U. Jensen and Helmut Lenzing
Title:
Model theoretic algebra
Additional book information:
Gordon & Breach, New York, 1989, 430 pp., $59.00. ISBN 2-88124-717-2
References:
- 1.
- J. W. Addison, L. Henkin, and A. Tarski (eds. ), The theory of models, Proceedings of the 1963 International Symposium at Berkeley, North-Holland, Amsterdam, 1965. MR 195680
- 2.
- A. Bauval, Polynomial rings and weak second-order logic, J. Symbolic Logic 50 (1985), 953-972. MR 820125
- 3.
- G. L. Cherlin, Model theoretic algebra, Selected Topics. Lecture Notes in Math., vol. 521, Springer-Verlag, Berlin, 1976. MR 539999
- 4.
- H. D. Ebbinghaus (ed. ), Ω-bibliography of mathematical logic, vol. III, Model Theory, Springer-Verlag, Berlin, 1987. MR 915633
- 5.
- M. Fried and M. Jarden, Field arithmetic, Springer-Verlag, Berlin, 1986. MR 868860
- 6.
- L. Henkin, Some interconnections between modern algebra and mathematical logic, Trans. Amer. Math. Soc. 74 (1953), 410-427. MR 55287
- 7.
- G. Hermann, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95 (1926), 736-788. MR 1512302
- 8.
- E. Hewitt, Rings of real-valued continuous functions, Trans. Amer. Math. Soc. 64 (1948), 45-99. MR 26239
- 9.
- G. Higman, B. H. Neumann, and H. Neumann, Embedding theorems for groups, J. London Math. Soc. 24 (149), 247-254. MR 32641
- 10.
- A. I. Maltsev, On the faithful representation of infinite groups by matrices, Mat. Sb. (NS) 8 (50) (1940), 405-422. (Russian)
- 11.
- A. I. Maltsev, A general method for obtaining local theorems in group theory, Uch Zap Ped Inst., Ivanovo 1 (1941), 3-9. (Russian) MR 75939
- 12.
- A. I. Maltsev, The metamathematics of algebraic systems, Collected papers: 1936-1967, North-Holland, Amsterdam, 1971. MR 349383
- 13.
- B. H. Neumann, Adjunction of elements to groups, J. London Math. Soc. 18 (1943), 4-11. MR 8808
- 14.
- M. Prest, Model theory and modules, London Mathematical Society Lecture Notes Series 130, Cambridge Univ. Press, Cambridge, 1988. MR 933092
- 15.
- A. Robinson, Introduction to model theory and to the metamathematics of algebra, North-Holland, Amsterdam, 1963. MR 153570
- 16.
- A. Robinson, Selected papers, vol. I: Model Theory and Algebra, Yale Univ. Press, New Haven, 1979. MR 533887
- 17.
- J. Robinson, The decision problem for fields, Proceedings of the 1963 International Symposium at Berkeley, pp. 299-311, North-Holland, Amsterdam, 1965. MR 200163
- 18.
- W. Szmielew, Decision problem in group theory, Internat. Congr. Philos., 1948, Amsterdam, North-Holland, Amsterdam, 1949, pp. 763-766. MR 28797
- 19.
- G. Takeuti, Two applications of logic to mathematics, Princeton Univ. Press, Princeton, NJ, 1978. MR 505474
- 20.
- A. Tarski, Sur les ensembles définissables de nombres réels. I, Fund. Math. 17 (1931), 210-239.
- 21.
- A. Tarski, A decision method for elementary algebra and geometry, Rand Corporation, Santa Monica, 1948. MR 28796
Additional Information:
Reviewer(s):
G.
Sabbagh
Review Information:
Journal:
Bull. Amer. Math. Soc.
25
(1991),
215-221.
DOI:
10.1090/S0273-0979-1991-16070-2
PII:
S 0273-0979(1991)16070-2
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