Bulletin of the American Mathematical Society

MathSciNet review: 1566989
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Greg Cherlin
Title: Model theoretic algebra: Selected topics
Additional book information: Lecture Notes in Mathematics, vol. 521, Springer-Verlag, Berlin and New York, 1976, iv + 232 pp., $9.50.

1.

C. C. Chang and J. Keisler, Model theory, North-Holland, Amsterdam, 1973.

G. L. Cherlin, Model theoretic algebra, J. Symbolic Logic 41 (1976), no. 2, 537–545. MR 411961, DOI 10.2307/2272254

3.

P. Eklof, Ultraproducts for algebraists, Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977.

Joram Hirschfeld and William H. Wheeler, Forcing, arithmetic, division rings, Lecture Notes in Mathematics, Vol. 454, Springer-Verlag, Berlin-New York, 1975. MR 0389581

Simon Kochen, The model theory of local fields, $\vDash$ISILC Logic Conference (Proc. Internat. Summer Inst. and Logic Colloq., Kiel, 1974) Lecture Notes in Math., Vol. 499, Springer, Berlin, 1975, pp. 384–425. MR 0568318

Handbook of mathematical logic, Studies in Logic and the Foundations of Mathematics, vol. 90, North-Holland Publishing Co., Amsterdam, 1977. With the cooperation of H. J. Keisler, K. Kunen, Y. N. Moschovakis and A. S. Troelstra. MR 457132

Abraham Robinson, Introduction to model theory and to the metamathematics of algebra, North-Holland Publishing Co., Amsterdam, 1963. MR 0153570

Abraham Robinson, On the notion of algebraic closedness for noncommutative groups and fields, J. Symbolic Logic 36 (1971), 441–444. MR 290949, DOI 10.2307/2269952

Abraham Robinson, Model theory as a framework for algebra, Studies in model theory, MAA Studies in Math., Vol. 8, Math. Assoc. Amer., Buffalo, N.Y., 1973, pp. 134–157. MR 0337596

Gerald E. Sacks, Saturated model theory, Mathematics Lecture Note Series, W. A. Benjamin, Inc., Reading, Mass., 1972. MR 0398817

11.

S. Shelah, The lazy model-theoretician's guide to stability, Proc. Louvain Model Theory Conf., Logique et Analyse, No. 71-72 (1975).

Carol Wood, The model theory of differential fields revisited, Israel J. Math. 25 (1976), no. 3-4, 331–352. MR 457199, DOI 10.1007/BF02757008

1.

C. C. Chang and J. Keisler, Model theory, North-Holland, Amsterdam, 1973.

2.

G. Cherlin, Model-theoretic algebra, J. Symbolic Logic 41 (1976), 537-545. MR 0411961

3.

P. Eklof, Ultraproducts for algebraists, Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977.

4.

J. Hirschfeld and W. Wheeler, Forcing, arithmetic, division rings, Lecture Notes in Math., vol. 454, Springer-Verlag, Berlin and New York, 1975. MR 52 # 10412. MR 389581

5.

S. Kochen, The model theory of local fields, Logic Conf. (Kiel, 1974), Lecture Notes in Math., vol. 499, Springer-Verlag, Berlin and New York, 1975. MR 568318

6.

A. Macintyre, Model completeness, Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977. MR 457132

7.

A. Robinson, Introduction to model theory and to the metamathematics of algebra, North-Holland, Amsterdam, 1963. MR 27 #3533. MR 153570

8.

A. Robinson, On the notion of algebraic closedness for noncommutative groups and fields, J. Symbolic Logic 36 (1971), 441-444. MR 45 #43. MR 290949

9.

A. Robinson, Model theory as a framework for algebra, Studies in Model Theory, MAA Studies in Math., vol. 8, Buffalo, N.Y., pp. 134-157, 1973. MR 49 #2365. MR 337596

10.

G. Sacks, Saturated model theory, Benjamin, New York, 1972. MR 398817

11.

S. Shelah, The lazy model-theoretician's guide to stability, Proc. Louvain Model Theory Conf., Logique et Analyse, No. 71-72 (1975).

12.

C. Wood, The model theory of differential fields revisited, Israel J. Math. 25 (1976), 331-352. MR 457199