Forcing for h$L$ and hd
Volume 88 / 2001
Colloquium Mathematicum 88 (2001), 273-310
MSC: Primary 03E35, 03G05, 54A25; Secondary 03E05, 06Exx.
DOI: 10.4064/cm88-2-9
Abstract
The present paper addresses the problem of attainment of the supremums in various equivalent definitions of the hereditary density ${\rm hd}$ and hereditary Lindelöf degree ${\rm hL}$ of Boolean algebras. We partially answer two problems of J. Donald Monk [13, Problems 50, 54], showing consistency of different attainment behaviour and proving that (for the variants considered) this is the best result we can expect.
