Abstract
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, 2ω. We further study some naturally ocurring examples of such partial orders.
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Balcar, B., Doucha, M. & Hrušák, M. Base Tree Property. Order 32, 69–81 (2015). https://doi.org/10.1007/s11083-013-9316-2
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DOI: https://doi.org/10.1007/s11083-013-9316-2