Does ${\bf SP}\ K\supseteq\ {\bf PS}\ K$ imply axiom of choice?
Commentationes Mathematicae Universitatis Carolinae, Tome 21 (1980) no. 4, pp. 699-706.

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Classification : 03E25, 04A25, 06A15, 08A05, 08A30, 08A99, 08C15, 08C99
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     author = {Andr\'eka, H. and N\'emeti, I.},
     title = {Does ${\bf SP}\ K\supseteq\ {\bf PS}\ K$ imply axiom of choice?},
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Andréka, H.; Németi, I. Does ${\bf SP}\ K\supseteq\ {\bf PS}\ K$ imply axiom of choice?. Commentationes Mathematicae Universitatis Carolinae, Tome 21 (1980) no. 4, pp. 699-706. http://geodesic.mathdoc.fr/item/CMUC_1980__21_4_a5/