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The diamond principle for the uniformity of the meager ideal implies the existence of a destructible gap

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Abstract

We prove the theorem from the title which answers a question addressed in the paper of Moore-Hrusak-Dzamonja [3].

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References

  1. Abraham, U., Todorčević, S.: Partition properties of ω1 compatible with CH. Fundamenta Mathematicae 152, 165–180 (1997)

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  2. Bartoszyński, T., Judah, H.: Set Theory: On the structure of the real line, A.K.Peters, Wellesley, Massachusetts, (1995)

  3. Moore, J., Hrušák, M., Džamonja, M.: Parametrized principles. Transactions of American Mathematical Society 356 (6), 2281–2306 (2004)

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  4. Scheepers, M.: Gaps in ωω. In: Set Theory of the Reals, volume 6 of Israel Mathematical Conference Proceedings, pp. 439–561 (1993)

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Authors and Affiliations

  1. Graduate School of Science and Technology, Kobe University, Rokkodai, Nada-ku, Kobe, 657-8501, Japan

    Teruyuki Yorioka

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  1. Teruyuki Yorioka
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Correspondence to Teruyuki Yorioka.

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Supported by JSPS Research Fellowshipsfor Young Scientists.

Supported by Grants-in-Aid for JSPS Fellow, No. 16.3977, Ministry of Education, Culture, Sports, Science and Technology.

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Yorioka, T. The diamond principle for the uniformity of the meager ideal implies the existence of a destructible gap. Arch. Math. Logic 44, 677–683 (2005). https://doi.org/10.1007/s00153-005-0280-4

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  • DOI: https://doi.org/10.1007/s00153-005-0280-4

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