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Patching ideal families and enforcing reflection

  • Christopher C. Leary (a1)

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For several years much research has been directed at ideals associated with large cardinals. In this paper we discuss ideal families and use this tool to investigate the saturation properties of various large cardinal ideals.

Much of the work in this paper is a direct outgrowth of material presented in my doctoral dissertation written at the University of Michigan under the patient guidance of Andreas Blass. I would also like to thank the referee for several helpful questions and comments on the original version of this paper.

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[B2]Baumgartner, J., Ineffability properties of cardinals. II, Logic, foundations of mathematics and computability theory (Proceedings of the fifth international congress on logic, methodology and philosophy of science, London, Ontario, 1975; Butts, R. E. and Hintikka, J., editors), Reidel, Dordrecht, 1977, pp. 87106.
[BTW]Baumgartner, J., Taylor, A., and Wagon, S., On splitting stationary subsets of large cardinals, this Journal, vol. 42 (1977), pp. 203214.
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[L1]Leary, C., Extensions of ideals on large cardinals, Ph.D. thesis, University of Michigan, Ann Arbor, Michigan, 1985.
[L2]Leary, C., Patching ideal families on large cardinals, Abstracts of Papers Presented to the American Mathematical Society, vol. 7 (1986), p. 7.
[M1]Mitchell, W., Sets constructible from sequences of ultrafilters, this Journal, vol. 39 (1974), pp. 5776.
[M2]Mitchell, W., Sets constructed from sequences of measures: revisited, this Journal, vol. 48 (1983), pp. 600609.

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Patching ideal families and enforcing reflection

  • Christopher C. Leary (a1)

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