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Hechler’s theorem for the null ideal

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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 Bartoszyński and Kada.

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References

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Prince Edward Island, Charlottetown PE, Canada, C1A 4P3

    Maxim R. Burke

  2. Department of Computer Sciences, Kitami Institute of Technology, Kitami, Hokkaido, 090-8507, Japan

    Masaru Kada

Authors
  1. Maxim R. Burke
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  2. Masaru Kada
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Corresponding author

Correspondence to Masaru Kada.

Additional information

Research supported by NSERC. The first author thanks F.D. Tall and the Department of Mathematics at the University of Toronto for their hospitality during the academic year 2003/2004 when the present paper was completed.

The second author was supported by Grant-in-Aid for Young Scientists (B) 14740058, MEXT.

Mathematics Subject Classification (2000): 03E35, 03E17

Revised version: 16 February 2004

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Burke, M., Kada, M. Hechler’s theorem for the null ideal. Arch. Math. Logic 43, 703–722 (2004). https://doi.org/10.1007/s00153-004-0224-4

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