A transfer theorem for nonstandard uniserials

Author:
Paul C. Eklof

Journal:
Proc. Amer. Math. Soc. **114** (1992), 593-600

MSC:
Primary 13L05; Secondary 03C60, 03E35, 03E75, 13C05

DOI:
https://doi.org/10.1090/S0002-9939-1992-1074751-8

MathSciNet review:
1074751

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A general theorem is described and proved which allows the transfer of results about the existence of nonstandard uniserial modules over a valuation domain from models of to all models of ZFC.

**[Ba]**J. Barwise,*An introduction to first-order logic*, Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977, pp. 5-46.**[BS1]**S. Bazzoni and L. Salce,*On nonstandard uniserial modules over valuation domains and their quotients*, J. Algebra**128**(1990), 292-305. MR**1036392 (91a:13012)****[BS2]**-,*Elongations of uniserial modules over valuation domains*, J. Algebra (to appear). MR**1152907 (93d:13033)****[BS3]**-,*Equimorphism classes of uniserial modules over valuation domains*, preprint.**[Fe]***Applications of many-sorted interpolation theorems*, Proceedings of the Tarski Symposium, Amer. Math. Soc., Providence, RI, 1974, pp. 205-224. MR**0406772 (53:10558)****[FS]**L. Fuchs and L. Salce,*Modules over valuation domains*, Marcel Dekker, New York, 1985. MR**786121 (86h:13008)****[FSh]**L. Fuchs and S. Shelah.*Kaplansky's problem on valuation rings*, Proc. Amer. Math. Soc.**105**(1989), 25-30. MR**929431 (89e:13030)****[MSh]**A. Mekler and S. Shelah,*Compactness for isomorphism quantifiers*, preprint.**[Sh1]**S. Shelah,*Models with second-order properties*. II,*Trees with no undefined branches*, Ann. of Math.**14**(1978), 73-87. MR**501098 (80b:03047b)****[Sh2]**-,*Nonstandard uniserial module over a uniserial domain exists*, Around Classification Theory of Models, Lecture Notes in Math., vol. 1182, Springer-Verlag, Berlin and New York (1986), 135-150. MR**850056**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
13L05,
03C60,
03E35,
03E75,
13C05

Retrieve articles in all journals with MSC: 13L05, 03C60, 03E35, 03E75, 13C05

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1992-1074751-8

Keywords:
Valuation domain,
uniserial,
nonstandard uniserial,
many-sorted language,
transfer theorem

Article copyright:
© Copyright 1992
American Mathematical Society