On invariants for 𝜔₁-separable groups

Eklof, Paul C.; Foreman, Matthew; Shelah, Saharon

doi:10.1090/S0002-9947-1995-1316849-X

On invariants for $\omega _ 1$-separable groups
HTML articles powered by AMS MathViewer

by Paul C. Eklof, Matthew Foreman and Saharon Shelah PDF

Trans. Amer. Math. Soc. 347 (1995), 4385-4402 Request permission

Abstract:

We study the classification of ${\omega _1}$-separable groups by using Ehrenfeucht-Fraïssé games and prove a strong classification result assuming PFA, and a strong non-structure theorem assuming $\diamondsuit$.

References

Paul C. Eklof, The structure of $\omega _{1}$-separable groups, Trans. Amer. Math. Soc. 279 (1983), no. 2, 497–523. MR 709565, DOI 10.1090/S0002-9947-1983-0709565-8
Paul C. Eklof and Alan H. Mekler, Almost free modules, North-Holland Mathematical Library, vol. 46, North-Holland Publishing Co., Amsterdam, 1990. Set-theoretic methods. MR 1055083
Tapani Hyttinen, Model theory for infinite quantifier languages, Fund. Math. 134 (1990), no. 2, 125–142. MR 1074640, DOI 10.4064/fm-134-2-125-142
Tapani Hyttinen and Heikki Tuuri, Constructing strongly equivalent nonisomorphic models for unstable theories, Ann. Pure Appl. Logic 52 (1991), no. 3, 203–248. MR 1111753, DOI 10.1016/0168-0072(91)90031-G
Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
Maaret Karttunen, Model theory for infinitely deep languages, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 50 (1984), 96. MR 761409
Alan H. Mekler, Proper forcing and abelian groups, Abelian group theory (Honolulu, Hawaii, 1983) Lecture Notes in Math., vol. 1006, Springer, Berlin, 1983, pp. 285–303. MR 722625, DOI 10.1007/BFb0103709
Alan H. Mekler, The structure of groups which are almost the direct sum of countable abelian groups, Trans. Amer. Math. Soc. 303 (1987), no. 1, 145–160. MR 896012, DOI 10.1090/S0002-9947-1987-0896012-2
Alan Mekler, Saharon Shelah, and Jouko Väänänen, The Ehrenfeucht-Fraïssé-game of length $\omega _1$, Trans. Amer. Math. Soc. 339 (1993), no. 2, 567–580. MR 1191613, DOI 10.1090/S0002-9947-1993-1191613-1
Alan Mekler and Juha Oikkonen, Abelian $p$-groups with no invariants, J. Pure Appl. Algebra 87 (1993), no. 1, 51–59. MR 1222176, DOI 10.1016/0022-4049(93)90068-5

Enrenfeucht-Fraïssé-games and nonstructure theorems

Games and trees in infinitary logic

a survey