Archive for Mathematical Logic

, Volume 40, Issue 2, pp 93–112 | Cite as

Groupwise dense families

  • Heike Mildenberger


We show that the Filter Dichotomy Principle implies that there are exactly four classes of ideals in the set of increasing functions from the natural numbers. We thus answer two open questions on consequences of ? < ?. We show that ? < ? implies that ? = ?, and that Filter Dichotomy together with ? < ? implies ? < ?. The technical means is the investigation of groupwise dense sets, ideals, filters and ultrafilters. With related techniques we prove the new inequality ?≤ cf(?).

Mathematics Subject Classification (2000): 03E35 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Heike Mildenberger
    • 1
  1. 1.Institute for Mathematics, The Hebrew University, Givat Ram, Jerusalem 91904, Israel. e-mail:

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