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International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 305-309
http://dx.doi.org/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 Hindawi Publishing Corporation. 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.