International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 305-309
doi:10.1155/S016117129500038X
On chains and posets within the power set of a continuum
Pure Mathematics Department, Queen's University, Belfast BT7 1NN, Ireland
Received 6 May 1993; Revised 27 October 1993
Copyright © 1995 P. T. Matthews and T. B. M. McMaster. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Transfinite induction is employed to construct a copy of an arbitrary partially-ordered
set of cardinality at most c within the power set (quasi-ordered by sub-chain
embeddability) of the real line.