Hechler’s theorem for the null ideal

@article{Burke2004HechlersTF,
  title={Hechler’s theorem for the null ideal},
  author={Maxim R. Burke and Masaru Kada},
  journal={Archive for Mathematical Logic},
  year={2004},
  volume={43},
  pages={703-722}
}
  • M. Burke, M. Kada
  • Published 15 November 2002
  • Mathematics
  • Archive for Mathematical Logic
Abstract.We prove the following theorem: For a partially ordered set Q such that every countable subset of Q has a strict upper bound, there is a forcing notion satisfying the countable chain condition such that, in the forcing extension, 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. The corresponding theorem for the meager ideal was established by… 
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