, Volume 32, Issue 1, pp 69–81 | Cite as

Base Tree Property

  • Bohuslav Balcar
  • Michal Doucha
  • Michael Hrušák


Building on previous work from Balcar et al., Fund. Math. 110, 11–24 (1980) we investigate σ-closed partial orders of size continuum. We provide both an internal and external characterization of such partial orders by showing that (1) every σ-closed partial order of size continuum has a base tree and that (2) σ-closed forcing notions of density 𝔠 correspond exactly to regular suborders of the collapsing algebra Coll(ω 1, 2 ω . We further study some naturally ocurring examples of such partial orders.


Forcing Boolean algebras Base tree 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Bohuslav Balcar
    • 1
  • Michal Doucha
    • 2
  • Michael Hrušák
    • 3
  1. 1.The Center for Theoretical StudyCharles University in PraguePragueCzech Republic
  2. 2.Institute of mathematicsAcademy of Sciences of the Czech republicPragueCzech Republic
  3. 3.Centro de Ciencias Matem’aticasUNAMMoreliaMéxico

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