Book Review
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MathSciNet review:
1568173
Full text of review:
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Book Information:
Author:
Wilfrid Hodges
Title:
Model theory
Additional book information:
{Encyclopedia of Mathematics and its Applications, vol.\ 42}, Cambridge University Press, Cambridge, 1993, xiii + 772 pp., US$99.95. ISBN 0-521-30442-3.
John T. Baldwin, Almost strongly minimal theories. I, II, J. Symbolic Logic 37 (1972), 487–493; ibid. 37 (1972), 657–660. MR 321722, DOI 10.2307/2272733
John T. Baldwin, Book Review: Classification theory and the number of non-isomorphic models, Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 2, 222–229. MR 1567308, DOI 10.1090/S0273-0979-1981-14891-6
J. T. Baldwin and A. H. Lachlan, On strongly minimal sets, J. Symbolic Logic 36 (1971), 79–96. MR 286642, DOI 10.2307/2271517
[4] C. C. Chang and H. J. Keisler, Model theory, North-Holland, Amsterdam, 1973.
[5] Bradd Hart, Classification theory and the number of nonisomorphic models (revised ed.) (reviewed by S. Shelah), J. Symbolic Logic 58 (1993), 1071-1074.
Ehud Hrushovski, A new strongly minimal set, Ann. Pure Appl. Logic 62 (1993), no. 2, 147–166. Stability in model theory, III (Trento, 1991). MR 1226304, DOI 10.1016/0168-0072(93)90171-9
[7] E. Hrushovski and Zeljko Sokolović, Minimal subsets of differentially closed fields (submitted).
Ehud Hrushovski and Boris Zilber, Zariski geometries, Bull. Amer. Math. Soc. (N.S.) 28 (1993), no. 2, 315–323. MR 1183999, DOI 10.1090/S0273-0979-1993-00380-X
J. Denef and L. van den Dries, $p$-adic and real subanalytic sets, Ann. of Math. (2) 128 (1988), no. 1, 79–138. MR 951508, DOI 10.2307/1971463
H. Jerome Keisler, Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers, Studies in Logic and the Foundations of Mathematics, Vol. 62, North-Holland Publishing Co., Amsterdam-London, 1971. MR 0344115
J. Łoś, On the categoricity in power of elementary deductive systems and some related problems, Colloq. Math. 3 (1954), 58–62. MR 61561, DOI 10.4064/cm-3-1-58-62
Angus Macintyre, On definable subsets of $p$-adic fields, J. Symbolic Logic 41 (1976), no. 3, 605–610. MR 485335, DOI 10.2307/2272038
Margit Messmer, Groups and fields interpretable in separably closed fields, Trans. Amer. Math. Soc. 344 (1994), no. 1, 361–377. MR 1231337, DOI 10.1090/S0002-9947-1994-1231337-6
Michael Morley, Categoricity in power, Trans. Amer. Math. Soc. 114 (1965), 514–538. MR 175782, DOI 10.1090/S0002-9947-1965-0175782-0
Saharon Shelah, Classification of first order theories which have a structure theorem, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 2, 227–232. MR 776474, DOI 10.1090/S0273-0979-1985-15354-6
[16] -, Classification theory and the number of nonisomorphic models, second ed., North-Holland, Amsterdam, 1991.
[17] Alfred Tarski, Sur les ensemble définissable de nombres réels i, Fund. Math. 17 (1931), 210-239.
[18] A. Wilkie, Model completeness results for expansions of the real field by restricted pfaffian functions and exponentiation (to appear).
[19] B. I. Zil'ber, Uncountably categorical theories, Transl. Math. Monographs, vol. 117, Amer. Math. Soc., Providence, RI, 1991.
- [1]
- J. T. Baldwin, Almost strongly minimal theories, J. Symbolic Logic 37 (1972), 487-493. MR 0321722 (48:89)
- [2]
- -, Classification theory and the number of nonisomorphic models (reviewed by S. Shelah), Bull. Amer. Math. Soc. (N.S.) 4 (1981), 222. MR 1567308
- [3]
- J. T. Baldwin and A. H. Lachlan, On strongly minimal sets, J. Symbolic Logic 36 (1971), 79-96. MR 0286642 (44:3851)
- [4]
- C. C. Chang and H. J. Keisler, Model theory, North-Holland, Amsterdam, 1973.
- [5]
- Bradd Hart, Classification theory and the number of nonisomorphic models (revised ed.) (reviewed by S. Shelah), J. Symbolic Logic 58 (1993), 1071-1074.
- [6]
- E. Hrushovski, A new strongly minimal set, Ann. Pure Appl. Logic 62 (1993), 147-166. MR 1226304 (94d:03064)
- [7]
- E. Hrushovski and Zeljko Sokolović, Minimal subsets of differentially closed fields (submitted).
- [8]
- Ehud Hrushovski and Boris Zilber, Zariski geometries, Bull. Amer. Math. Soc. (N.S.) 28 (1993), 315-324. MR 1183999 (93j:14003)
- [9]
- J. Denef and L. van den Dries, p-Adic and real subanalytic sets, Ann. of Math. (2) 128 (1988), 79-138. MR 951508 (89k:03034)
- [10]
- H. J. Keisler, Model theory for infinitary logic, North-Holland, Amsterdam, 1971. MR 0344115 (49:8855)
- [11]
- J. Los, On the categoricity in power of elementary deductive systems and related problems, Colloq. Math. 3 (1954), 58-62. MR 0061561 (15:845c)
- [12]
- Angus J. Macintyre, On definable subsets of p-adic fields, J. Symbolic Logic 41 (1976), 605-610. MR 0485335 (58:5182)
- [13]
- M. Messmer, Groups and fields interpretable in separably closed fields, Trans. Amer. Math. Soc. 344 (1994), 361-379. MR 1231337 (95c:03086)
- [14]
- M. Morley, Categoricity in power, Trans. Amer. Math. Soc. 114 (1965), 514-538. MR 0175782 (31:58)
- [15]
- S. Shelah, Classification of first order theories which have a structure theory, Bull. Amer. Math. Soc. (N.S.) 12 (1985), 227-232. MR 776474 (86h:03058)
- [16]
- -, Classification theory and the number of nonisomorphic models, second ed., North-Holland, Amsterdam, 1991.
- [17]
- Alfred Tarski, Sur les ensemble définissable de nombres réels i, Fund. Math. 17 (1931), 210-239.
- [18]
- A. Wilkie, Model completeness results for expansions of the real field by restricted pfaffian functions and exponentiation (to appear).
- [19]
- B. I. Zil'ber, Uncountably categorical theories, Transl. Math. Monographs, vol. 117, Amer. Math. Soc., Providence, RI, 1991.
Review Information:
Reviewer:
John T. Baldwin
Journal:
Bull. Amer. Math. Soc.
32 (1995), 280-285
DOI:
https://doi.org/10.1090/S0273-0979-1995-00578-1
