2002/11/30 by Maxim R. Burke, Masaru Kada
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Banach Space Theory #Advanced Topology and Set Theory #math.LO #msc:03E17 #msc:03E35
paper · pdf · doi:10.1007/s00153-004-0224-4
published as Arch. Math. Logic, Vol. 43(2004), pp. 703--722. · v8: Minor corrections
arxiv created 2004/02/22 · openalex publication_date 2004/04/22 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler's classical result in the theory of forcing, and the statement of the theorem for the meager ideal has been already proved by Bartoszynski and the author.