On strong chains of uncountable functions
Let \(f,g:\omega_1\rightarrow \omega_1\). Define \(f\ll g\) if and only if \(\{\xi\in\omega_1 : f(\xi)\geq g(\xi)~\}\) is finite. Answering a question of A. Hajnal, the author proves that the following is consistent: there is a well-ordered, increasing \(\ll\)-chain of length \(\omega_2\). The author uses his method of forcing with side conditions in morasses to establish this consistency result. Assuming CH, he also proves that no c.c.c forcing would give such a chain. The paper is meant to be self-contained.
scientific article; zbMATH DE number 1506591
scientific article