Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-12-01T07:17:49.740Z Has data issue: false hasContentIssue false
  • English
  • Français

as an initial segment of the c-degrees

Published online by Cambridge University Press:  12 March 2014

Marcia Groszek
Marcia Groszek*
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755
Get access Rights & Permissions [Opens in a new window]

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

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 3 , September 1994 , pp. 956 - 976
Copyright
Copyright © Association for Symbolic Logic 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[Al]Adamowicz, Zofia, On finite lattices of degrees of constructibility of reals, this Journal, vol. 41 (1976), pp. 313–322.Google Scholar
[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.CrossRefGoogle Scholar
[BL]Baumgartner, James E. and Laver, Richard, Iterated perfect set forcing, Annals of Mathematical Logic, vol. 17 (1979), pp. 271–288.CrossRefGoogle Scholar
[Gr]Grigorieff, S., Combinatorics on ideals and forcing, Annals of Mathematical Logic, vol. 3 (1971), pp. 363–394.CrossRefGoogle Scholar
[G]Groszek, Marcia, Applications of iterated perfect set forcing, Annals of Pure and Applied Logic, vol. 39 (1988), pp. 19–53.CrossRefGoogle Scholar
[GJ]Groszek, Marcia and Jech, Thomas, Generalized iteration of forcing, Transactions of the American Mathematical Society, vol. 324 (1991), pp. 1–26.CrossRefGoogle Scholar
[GL]Groszek, Marcia and Laver, Richard, Finite groups of OD-conjugates, Periodica Mathematica Hungarica, vol. 18 (1987), pp. 87–97.CrossRefGoogle Scholar
[GS]Groszek, Marcia and Shore, Richard A., Initial segments of the degrees of constructibility, Israel Journal of Mathematics, vol. 63 (1988), pp. 149–177.CrossRefGoogle Scholar
[Le]Lerman, Manuel. Initial segments of the degrees of unsolvability, Annals of Mathematics,. vol. 93 (1971), pp. 365–389.CrossRefGoogle Scholar
[L1]Lubarsky, Robert, Lattices of c-degrees, Annals of Pure and Applied Logic, vol. 36 (1987), pp. 115–118.CrossRefGoogle Scholar
[L2]Lubarsky, Robert, Definability and initial segments of c-degrees, this Journal, vol. 53 (1988), pp. 1070–1081.Google Scholar
[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.Google Scholar