##
**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 **R**^{n} are decomposed into countably many classes L_{0},L_{1},.... Then there is a decomposition of **R**^{n} into classes S_{0},S_{1},... such that if \ell is a line from L_{i} then \ell meets S_{i} 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

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag