The Fréchet-Urysohn compactum without points of countable character (Q578637)

In the world obtained by adding various Cohen subsets of \(\omega\) to ZFC, we have many mathematical objects with interesting properties. The author's main result is as follows: By adding a Cohen subset of \(\omega\) to ZFC the extended model contains a compactum (compact \(T_ 2\)-space) such that the tightness is countable and the character of any point is \(\aleph_ 1\). The following conclusion of this main theorem is obtained. Under Martin axiom \(+\rceil CH\), the same world contains a Fréchet- Urysohn compactum without points of countable character. The author proves this under Booth lemma (LB) implied from Martin axiom \(+\rceil CH\).