论文信息 - Vive la Différence I: Nonisomorphism of Ultrapowers of Countable Models - 字舞流文

Vive la Différence I: Nonisomorphism of Ultrapowers of Countable Models

We show that it is not provable in ZFC that any two countable elementarily equivalent structures have isomorphic ultrapowers relative to some ultrafilter on ω.

[1] Saharon Shelah,et al. Classification theory - and the number of non-isomorphic models, Second Edition , 1990, Studies in logic and the foundations of mathematics.

[2] Saharon Shelah,et al. Every two elementarily equivalent models have isomorphic ultrapowers , 1971 .

[3] W. Hodges. CLASSIFICATION THEORY AND THE NUMBER OF NON‐ISOMORPHIC MODELS , 1980 .

[4] H. Jerome Keisler,et al. Ultraproducts and Saturated Models , 1964 .

[5] S. Kochen,et al. Diophantine Problems Over Local Fields I , 1965 .

[6] Saharon Shelah,et al. A weak version of ◊ which follows from 2ℵ0<2ℵ1 , 1978 .

[7] Saharon Shelah. More on Proper Forcing , 1984, J. Symb. Log..

[8] Saharon Shelah. Models with second order properties. III. Omitting types forL(Q) , 1981, Arch. Math. Log..

[9] John Gregory,et al. Higher Souslin trees and the generalized continuum hypothesis , 1976, Journal of Symbolic Logic.

[10] Saharon Shelah,et al. Pointwise compact and stable sets of measurable functions , 1992, Journal of Symbolic Logic.

[11] Saharon Shelah,et al. Models with Second Order Properties V: A General Principle , 1993, Ann. Pure Appl. Log..

[12] Saharon Shelah,et al. Products of regular cardinals and cardinal invariants of products of Boolean algebras , 1990 .

[13] Saharon Shelah,et al. Models with second order properties IV. A general method and eliminating diamonds , 1983, Ann. Pure Appl. Log..