An ordered set of size \(\aleph_1\) with monochromatic maximal chains
The authors show that there are two linear orders, each of cardinality \(\aleph_1\), such that its product \(P\) has the following property: For every \(A\subset P\), \(A\) or \(P\setminus A\) contains a maximal chain. The result is obtained by sharpening tools which had been used in an earlier paper by the authors to show the above result assuming the continuum hypothesis.
scientific article; zbMATH DE number 1587193