An ordered set of size \(\aleph_1\) with monochromatic maximal chains (Q5929968)

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.