Abstract
AssumeV=L, or even ◊ M 1, there is no uncountable locally finite group which can be embedded in every uncountable universal locally finite group. Similar results hold for existentially closed groups and division rings.
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References
G. Baumslag,On the residual finiteness of generalised free products of nilpotent groups, Trans. Amer. Math. Soc.106(1963), 193–209.
M. Boffa,A note on existentially complete division rings, to appear in a Springer Lecture Notes volume edited by Saracino and Weisspfenning, in memory of Abraham Robinson.
M. Boffa and P. Van Praag,Sur les sous-champs maximaux des corps génériques dénombrable, C. R. Acad. Sc. Paris275(1972), 947–947.
K. Devlin,Aspects of Constructibility, Springer Lecture Notes in Mathematics, Vol. 354, Berlin-Heidelberg-New York, 1973.
P. Hall,Some constructions for locally finite groups, J. London Math. Soc.34(1959), 305–319.
J. Hirschfeld and W. H. Wheeler,Forcing, arithmetic, division rings, Springer Lecture Notes in Mathematics, Vol. 454, Berlin-Heidelberg-New York, 1975.
O. Kegel and B. Wehrfritz,Locally Finite Groups, North Holland, 1973.
A Macintyre and S. Shelah,Uncountable universal locally finite groups, submitted to J. Algebra.
B. H. Neumann,On amalgams of periodic groups, Proc. Roy. Soc. London, Ser. A255(1960), 477–489.
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Macintyre, A. Existentially closed structures and Jensen’s principle. Israel J. Math. 25, 202–210 (1976). https://doi.org/10.1007/BF02757000
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DOI: https://doi.org/10.1007/BF02757000