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On the structure of Δ 41 -sets of reals

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Abstract

Assuming that an inaccessible cardinal exists, we construct a ZFC-model where every Δ 41 -set is measurable but there exists a Δ 41 -set without the property of Baire. By a result of Shelah, an inaccessible cardinal is necessary for this result.

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References

  • [BaWo] Bagaria, J., Woodin, H.: Δ 1 n -sets of reals. J Symb Logic (to appear)

  • [Ba] Bartoszyński, T.: Additivity of measure implies additivity of category. Trans AMS281, 209–213 (1988)

    Google Scholar 

  • [BaJu] Bartoszyński, T., Judah, H.: Advanced set theory. Peters (to appear)

  • [BeJeWe] Beller, A., Jensen, R.B., Welch, P.: Coding the Universe. London: Cambridge University Press 1981

    Google Scholar 

  • [Da1] David, R.: Δ 13 -reals. Ann Math Logic23, 121–125 (1982)

    Google Scholar 

  • [Da2] David, R.: A very absolute Π 12 real singleton. Ann Math Logic23 101–120 (1982)

    Google Scholar 

  • [Ju] Judah, H.: Δ 13 -sets of reals. Israel Math Conf Proc6, 563–581 (1992)

    Google Scholar 

  • [JuSh1] Judah, H., Shelah, S.: Δ 12 -sets of reals. Ann Pure Appl Logic42, 207–233 (1989)

    Google Scholar 

  • [JuSh2] Judah, H., Shelah, S.: Δ 13 -sets of reals. J Symb Logic (to appear)

  • [JuSh3] Judah, H., Shelah, S.: Souslin forcing. J Symb Logic53, 1188–1207 (1988)

    Google Scholar 

  • [JuSp] Judah, H., Spinas, O.: Large cardinals and projective sets. To appear

  • [MaSo] Martin, D., Solovay, R.: Internal Cohen extensions. Ann Math Logic2, 143–178 (1970)

    Google Scholar 

  • [Ra] Raisonnier, J.: A mathematical proof of S. Shelah's theorem on the measure problem and related results. Israel J Math48, 48–56 (1984)

    Google Scholar 

  • [RaSt] Raisonnier, J., Stern, J.: The strength of measurability hypotheses. Israel J Math50, 337–349 (1985)

    Google Scholar 

  • [Sh] Shelah, S.: Can you take Solovay's inaccessible away? Israel J Math48, 1–47 (1984)

    Google Scholar 

  • [So] Solovay, R.: A model of set theory in which every set of reals is Lebesgue measurable. Ann Math92, 1–56 (1970)

    Google Scholar 

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The author is partially supported by the Basic Research Foundation of the Israel Academy of Sciences and by the Swiss National Funds.

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Judah, H., Spinas, O. On the structure of Δ 41 -sets of reals. Arch Math Logic 34, 301–312 (1995). https://doi.org/10.1007/BF01387510

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  • DOI: https://doi.org/10.1007/BF01387510

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