Efimovʼs problem and Boolean algebras

We continue the study, started by P. Koszmider, of a class of Boolean algebras, the so-called T -algebras. We prove the following.(1) peratomic Boolean algebras belong to this class. lass is contained properly in Koppelbergʼs class of minimally generated Boolean algebras. istence of an Efimov T -algebra (i.e., a T -algebra whose Stone space is infinite and contains no converging sequence and no copy of βω) implies a negative answer to Scarborough–Stoneʼs problem. is an Efimov T -algebra of countable tightness in the generic extension obtained by a finite support iteration of length ω 2 of Hechlerʼs poset over a model of CH.