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Σ½-sets of reals

Published online by Cambridge University Press:  12 March 2014

Jaime I. Ihoda
Jaime I. Ihoda*
Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem, Israel Universidad Católica de Chile, Santiago, Chile
*
Department of Mathematics, University of California, Berkeley, California 94720
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Abstract

We prove that the only implications between four notions for Σ½-sets of reals are

Type
Survey/expository papers
Information
The Journal of Symbolic Logic , Volume 53 , Issue 2 , June 1988 , pp. 636 - 642
Copyright
Copyright © Association for Symbolic Logic 1988

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References

REFERENCES

[1] Baumgartner, J., Iterated forcing, Surveys in set theory (Mathias, A. R. D., editor), London Mathematical Society Lecture Note Series, No. 8, Cambridge University Press, Cambridge, 1983.Google Scholar
[2] Baumgartner, J. and Dordal, P., Adjoining dominating functions, this Journal, vol. 50 (1985), pp. 94–101.Google Scholar
[3] Ellentuck, E., A new proof that analytic sets are Ramsey, this Journal, vol. 39 (1974), pp. 163–165.Google Scholar
[4] Galvin, F., Mycielski, J. and Solovay, R., Strong measure zero sets, Notices of the American Mathematical Society, vol. 26 (1979), p. A–280.Google Scholar
[5] Galvin, F. and Prikry, K., Borel sets and Ramsey's theorem, this Journal, vol. 38 (1973), pp. 193–198.Google Scholar
[6] Ihoda, J., Some consistency results on projective sets of reals, Israel Journal of Mathematics (submitted).Google Scholar
[7] Ihoda, J. and Shelah, S., Souslin forcing, this Journal (to appear).Google Scholar
[7a] Jech, T., Set theory, Academic Press, New York, 1978.Google Scholar
[8] Kechris, A., Measure and category in effective descriptive set theory, Annals of Mathematical Logic, vol. 5 (1973), pp. 337–384.CrossRefGoogle Scholar
[9] Kechris, A., On a notion of smallness for subsets of the Baire space, Transactions of the American Mathematical Society, vol. 229 (1977), pp. 191–207.CrossRefGoogle Scholar
[10] Mathias, A. R. D., Happy families, Annals of Mathematical Logic, vol. 12 (1977), pp. 59–111.CrossRefGoogle Scholar
[11] Miller, A, Some properties of measure and category, Transactions of the American Mathematical Society, vol. 266 (1981), pp. 93–114.CrossRefGoogle Scholar
[12] Raisonnier, J. and Stern, J., The strength of measurability hypotheses, Israel Journal of Mathematics, vol. 50 (1985), pp. 337–349.CrossRefGoogle Scholar
[13] Shelah, S., Can you take Solovay's inaccessible away, Israel Journal of Mathematics, vol. 48 (1984), pp. 1–47.CrossRefGoogle Scholar
[14] Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin, 1982.CrossRefGoogle Scholar
[15] Shelah, S., On cardinal invariants of the continuum, Axiomatic set theory, Contemporary Mathematics, vol. 31, American Mathematical Society, Providence, Rhode Island, 1984, pp. 183–207.CrossRefGoogle Scholar
[16] Silver, J., Every analytic set is Ramsey, this Journal, vol. 35 (1970), pp. 60–64.Google Scholar
[17] Stern, J., Regularity properties of definable sets of reals, Annals of Pure and Applied Logic, vol. 29 (1985), pp. 289–324.CrossRefGoogle Scholar