Forcing for h$L$ and hd

Tom 88 / 2001

Andrzej Rosłanowski, Saharon Shelah Colloquium Mathematicum 88 (2001), 273-310 MSC: Primary 03E35, 03G05, 54A25; Secondary 03E05, 06Exx. DOI: 10.4064/cm88-2-9


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.


  • Andrzej RosłanowskiDepartment of Mathematics
    University of Nebraska at Omaha
    Omaha, NE 68182-0243, U.S.A.
    Mathematical Institute
    Wrocław University
    50384 Wroclaw, Poland
  • Saharon ShelahInstitute of Mathematics
    The Hebrew University of Jerusalem
    91904 Jerusalem, Israel
    Department of Mathematics
    Rutgers University
    New Brunswick, NJ 08854, U.S.A.

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