Countable models of stable theories

Author:
Anand Pillay

Journal:
Proc. Amer. Math. Soc. **89** (1983), 666-672

MSC:
Primary 03C45; Secondary 03C15

DOI:
https://doi.org/10.1090/S0002-9939-1983-0718994-3

MathSciNet review:
718994

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Abstract: The notion of a normal theory such a theory . theorem that for superstable stronger than stability but incomparable is introduced, and it is proved that for We also include a short proof of Lachlan's (The property of normality is to superstability.)

**[1]**A. H. Lachlan,*The number of countable models of a countable superstable theory*, Proc. Internat. Congr. on Logic, Methodology and the Philosophy of Science, North-Holland, Amsterdam, 1973. pp. 45-56. MR**0446949 (56:5266)****[2]**-,*Two conjectures on the stability of**-categorial theories*, Fund. Math.**81**(1974), 133-145.**[3]**D. Lascar,*Ranks and definability in superstable theories*, Israel J. Math.**23**(1976), 53-87. MR**0409169 (53:12931)****[4]**D. Lascar and B. Poizat,*An introduction to forking*, J. Symbolic Logic**44**(1979), 330-350. MR**540665 (80k:03030)****[5]**T. G. Mustafin,*Number of countable models of a countable complete theory*, Algebra i Logika**20**(1981), 69-91. MR**635651 (84m:03047)****[6]**A. Pillay,*Countable modules*, Fund. Math. (to appear). MR**765328 (86c:03029)****[7]**S. Shelah,*Classification theory and the number of non-isomorphic models*, North-Holland, Amsterdam, 1978. MR**513226 (81a:03030)**

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DOI:
https://doi.org/10.1090/S0002-9939-1983-0718994-3

Keywords:
Normal theory,
superstable

Article copyright:
© Copyright 1983
American Mathematical Society