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as an initial segment of the c-degrees

  • Marcia Groszek (a1)

Abstract

By an “inverse iteration” of Sacks forcing over a model of V = L, we produce a model in which the degrees of constructibility of nonconstructible reals have order type

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[Al]Adamowicz, Zofia, On finite lattices of degrees of constructibility of reals, this Journal, vol. 41 (1976), pp. 313–322.
[A2]Adamowicz, Zofia, Constructible semi-lattices of degrees of constructibility, Set theory and hierarchy theory V (Lachlan, , Srebny, , and Zarach, , editors), Lecture Notes in Mathematics, vol. 619, Springer-Verlag, Berlin, 1977, pp. 1–44.
[BL]Baumgartner, James E. and Laver, Richard, Iterated perfect set forcing, Annals of Mathematical Logic, vol. 17 (1979), pp. 271–288.
[Gr]Grigorieff, S., Combinatorics on ideals and forcing, Annals of Mathematical Logic, vol. 3 (1971), pp. 363–394.
[G]Groszek, Marcia, Applications of iterated perfect set forcing, Annals of Pure and Applied Logic, vol. 39 (1988), pp. 19–53.
[GJ]Groszek, Marcia and Jech, Thomas, Generalized iteration of forcing, Transactions of the American Mathematical Society, vol. 324 (1991), pp. 1–26.
[GL]Groszek, Marcia and Laver, Richard, Finite groups of OD-conjugates, Periodica Mathematica Hungarica, vol. 18 (1987), pp. 87–97.
[GS]Groszek, Marcia and Shore, Richard A., Initial segments of the degrees of constructibility, Israel Journal of Mathematics, vol. 63 (1988), pp. 149–177.
[Le]Lerman, Manuel. Initial segments of the degrees of unsolvability, Annals of Mathematics,. vol. 93 (1971), pp. 365–389.
[L1]Lubarsky, Robert, Lattices of c-degrees, Annals of Pure and Applied Logic, vol. 36 (1987), pp. 115–118.
[L2]Lubarsky, Robert, Definability and initial segments of c-degrees, this Journal, vol. 53 (1988), pp. 1070–1081.
[S]Sacks, Gerald E.. Forcing with perfect closed sets, Axiomatic set theory, Part I, Proceedings of Symposia in Pure Mathematics, vol. 13. American Mathematical Society, Providence, Rhode Island, 1971, pp. 331–355.

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as an initial segment of the c-degrees

  • Marcia Groszek (a1)

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