On the independent subsets of a closure system with singular dimension (Q1073054)

This paper examines the question to what extent it is possible to generalize to arbitrary closure systems the following known result: If the cofinality of a partially ordered set (E,\(\leq)\) is a singular cardinal, then E contains an infinite antichain. The main result of the paper says that if \({\mathcal C}\) is a closure system having singular dimension, then there are arbitrarily large finite \({\mathcal C}\)-independent sets.