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A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals. (English) Zbl 0369.02034

MSC:
03C60 Model-theoretic algebra
03E35 Consistency and independence results
03C75 Other infinitary logic
03E99 Set theory
20A10 Metamathematical considerations in group theory
05A05 Permutations, words, matrices
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[1] J. Baumgartner,A new kind of order types (preprint).
[2] C. C. Chang,Some Remarks on the Model Theory of Infinitary Languages; the Syntax and Semantics of Infinitary Languages, ed. Barwise, Springer-Verlag Lecture Notes No. 72, 1968, pp. 36–63.
[3] P. Eklof,Infinitary equivalence of abelian groups, Fund. Math., to appear. · Zbl 0327.02050
[4] P. Eklof,On the existence of \(\kappa\)-free abelian groups, to appear. · Zbl 0268.20036
[5] P. Eklof,Theorem of ZFCon abelian groups infinitarily equivalent to free groups, Notices Amer. Math. Soc.20 (1973), A-503.
[6] P. Erdös and A. Hajnal,Unsolved problems in set theory, Proc. Symp. Pure Math. XIII, Part I, Amer. Math. Soc., Providence, R. I., 1971, pp. 17–48. · Zbl 0228.04001
[7] P. Erdös and A. Hajnal,Unsolved and solved problems in set theory, Proc. Symp. in Honour of Tarski’s 70th Birthday, Berkeley, 1971; Proc. Symp. Pure Math. XXV, Amer. Math. Soc., Providence, R. I., 1974, 269–288.
[8] L. Fuchs,Infinite Abelian Groups, Vol. I, 1970, Vol. II, 1973, Academic Press, N. Y. and London. · Zbl 0209.05503
[9] W. Hanf,Incompactness in languages with infinitely long expressions, Fund. Math.53 (1963/64), 309–324. · Zbl 0207.30201
[10] P. Hill,New criteria for freeness in abelian groups, II. · Zbl 0296.20026
[11] P. Hill,On the freeness of abelian groups: a generalization of Pontryagin’s theorem, Bull. Amer. Math. Soc.76 (1970), 1118–1120. · Zbl 0223.20058 · doi:10.1090/S0002-9904-1970-12586-1
[12] P. Hill,A special criterion for freeness. · Zbl 0295.20061
[13] P. Hill,The splitting of modules and abelian groups, Canad. J. Math.
[14] G. Higman,Almost free groups, Proc. London Math. Soc.3, 1, (1951), 284–290. · Zbl 0043.25701 · doi:10.1112/plms/s3-1.1.284
[15] J. Gregory,Abelian groups infinitarily equivalent to free ones, Notices Amer. Math. Soc.20 (1973), A-500.
[16] P. Griffith, n-free abelian groups, Aarhus University preprint series, 1971/72.
[17] R. L. Jensen,The fine structure of the constructible universe, Ann. Math. Logic4 (1972), 229–308. · Zbl 0257.02035 · doi:10.1016/0003-4843(72)90001-0
[18] A. Kurosch,Teoriya Grup, Moscow-Leningrad, 1944.
[19] A. Kurosch,The Theory of Groups, Chelsea Publ. Co., N. Y., 1960. · Zbl 0064.25104
[20] D. M. Kueker,Free and almost free algebra, Bull. Amer. Math. Soc., to appear. · Zbl 0204.31002
[21] E. Milner and S. Shelah,Two theorems on transversals, Proc. Symp. in Honour of Erdös’ 60th Birthday, Hungary, 1973, to appear. · Zbl 0322.05004
[22] E. Milner and S. Shelah,Sufficiency conditions for the existence of transversals, Canad. J. Math.26 (1974), 948–961. · Zbl 0303.05003 · doi:10.4153/CJM-1974-089-8
[23] N. Mirsky,Transversal Theory, Academic Press, New York, 1971.
[24] A. Mekler, Ph. D. thesis, Stanford University, in preparation.
[25] S. Shelah,Notes in partition calculus, Proc. Symp. in Honour of Erdös’ 60th Birthday, Hungary, 1973, to appear. · Zbl 0267.04006
[26] S. Shelah,Infinite abelian groups–Whitehead problem and some constructions, Israel J. Math.18 (1974), 243–256. · Zbl 0318.02053 · doi:10.1007/BF02757281
[27] S. Shelah,Compactness in singular cardinalities, Notices Amer. Math. Soc.21 (1974), A-556.
[28] S. Shelah,Stability and Number of Non-isomorphic Models, North Holland Publ. Co., to appear. · Zbl 0713.03013
[29] S. Shelah,Incompactness in regular cardinals, in preparation. · Zbl 0617.03025
[30] S. Shelah,Various results in mathematical logic, Notices Amer. Math. Soc.22 (1975), A-23.
[31] S. Shelah,Various results in mathematical logic, Notices Amer. Math. Soc.22 (1975), A-474.
[32] E. Specker,Additive Gruppen von Fongen Ganzer Zahlen, Portugal. Math.9 (1950), 131–140. · Zbl 0041.36314
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