## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  882.03031
Autor:  Erdös, Paul; Jackson, Steve; Mauldin, R.Daniel
Title:  On infinite partitions of lines and space. (In English)
Source:  Fundam. Math. 152, No.1, 75-95 (1997).
Review:  Assume Martin's axiom and that the lines of the euclidean space Rn are decomposed into countably many classes L0,L1,.... Then there is a decomposition of Rn into classes S0,S1,... such that if \ell is a line from Li then \ell meets Si in at most 3 points. Several other results extend this and earlier theorems to the case when higher dimensional hyperplanes are considered in place of lines.
Reviewer:  P.Komjath (Burnaby)
Classif.:  * 03E05 Combinatorial set theory (logic)
03E50 Continuum hypothesis and generalizations (logic)
04A20 Combinatorial set theory
Keywords:  Martin's axiom; transfinite recursion; set theoretic constructions in euclidean spaces

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