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Hodges, Wilfrid

In singular cardinality, locally free algebras are free. (English) Zbl 0476.03039

Algebra Univers. 12, 205-220 (1981).
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Cited in 1 Review
Cited in 28 Documents

MSC:

03C60 Model-theoretic algebra
08B20 Free algebras
20E10 Quasivarieties and varieties of groups
20K15 Torsion-free groups, finite rank
20A15 Applications of logic to group theory

Keywords:

free subgroups; singular cardinal; games; Schreier property; nilpotent variety of groups

Citations:

Zbl 0369.02034; Zbl 0264.02017
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Full Text: DOI

References:

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[2] Paul C. Eklof On the existence of {\(\kappa\)}-free abelian groups, Proc. Amer. Math. Soc.47 (1975) 65–72. · Zbl 0268.20036
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[5] Kenneth K. Hickin,Countable type local theorems in algebra, J. Algebra27 (1973), 523–537. · Zbl 0275.08005 · doi:10.1016/0021-8693(73)90062-8
[6] Kenneth K. Hickin andRichard E. Phillips,Local theorems and group extensions, Proc. Camb. Phil. Soc.73 (1973) 7–20. · Zbl 0248.20038 · doi:10.1017/S030500410004740X
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[8] Paul Hill,Primary groups whose subgroups of smaller cardinality are direct sums of cyclic groups, Pacific J. Math.42 (1972) 63–67. · Zbl 0251.20057
[9] Paul Hill,A special criterion for freeness, Symposia Math.13 (1974) 311–314.
[10] Howard L. Hiller, Martin Huber andSaharon Shelah,The structure of Ext(A, Z) and V=L, Math. Z.162 (1978) 39–50. · doi:10.1007/BF01437821
[11] Thomas J. Jech,Some combinatorial problems concerning uncountable cardinals, Annals of Math. Logic5 (1973) 165–198. · Zbl 0262.02062 · doi:10.1016/0003-4843(73)90014-4
[12] David W. Kueker,Löwenheim-Skolem and interpolation theorems in infinitary languages, Bull. Amer. Math. Soc.78 (1972) 211–215. · Zbl 0264.02017 · doi:10.1090/S0002-9904-1972-12921-5
[13] David W. Kueker,Countable approximations and Löwenheim-Skolem theorems, Annals of Math. Logic11 (1977) 57–103. · Zbl 0364.02009 · doi:10.1016/0003-4843(77)90010-9
[14] Hanna Neumann,Varieties of groups, Springer-Verlag, Berlin 1967. · Zbl 0251.20001
[15] Peter M. Neumann andJames Wiegold,Schreier varieties of groups, Math. Z.85 (1964) 392–400. · Zbl 0126.26901 · doi:10.1007/BF01115359
[16] Derek J. S. Robinson,Finiteness conditions and generalized soluble groups, Part 2, Springer-Verlag, Berlin 1972. · Zbl 0243.20033
[17] Saharon Shelah,A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals, Israel J. Math.21 (1975) 319–349. · Zbl 0369.02034 · doi:10.1007/BF02757993
[18] Ernst Witt,Die Unterringe der freien Lieschen Ringe, Mat. Z.64 (1956) 195–216. · Zbl 0070.02903 · doi:10.1007/BF01166568
[19] Oscar Zariski,On Castelnuovo’s criterion of rationality p a=P2=0 of an algebraic surface, Illinois J. Math.2 (1958), 303–315. · Zbl 0085.36203
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