Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

More About Uniform Upper Bounds on Ideals of Turing Degrees

Harold T. Hodes
The Journal of Symbolic Logic
Vol. 48, No. 2 (Jun., 1983), pp. 441-457
DOI: 10.2307/2273561
Stable URL: http://www.jstor.org/stable/2273561
Page Count: 17
  • Read Online (Free)
  • Download ($10.00)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
More About Uniform Upper Bounds on Ideals of Turing Degrees
Preview not available

Abstract

Let I be a countable jump ideal in $\mathscr{D} = \langle \text{The Turing degrees}, \leq\rangle$. The central theorem of this paper is: a is a uniform upper bound on I iff a computes the join of an I-exact pair whose double jump a(1) computes. We may replace "the join of an I-exact pair" in the above theorem by "a weak uniform upper bound on I". We also answer two minimality questions: the class of uniform upper bounds on I never has a minimal member; if ∪ I = Lα[ A] ∩ ωω for α admissible or a limit of admissibles, the same holds for nice uniform upper bounds. The central technique used in proving these theorems consists in this: by trial and error construct a generic sequence approximating the desired object; simultaneously settle definitely on finite pieces of that object; make sure that the guessing settles down to the object determined by the limit of these finite pieces.

Page Thumbnails

  • Thumbnail: Page 
441
    441
  • Thumbnail: Page 
442
    442
  • Thumbnail: Page 
443
    443
  • Thumbnail: Page 
444
    444
  • Thumbnail: Page 
445
    445
  • Thumbnail: Page 
446
    446
  • Thumbnail: Page 
447
    447
  • Thumbnail: Page 
448
    448
  • Thumbnail: Page 
449
    449
  • Thumbnail: Page 
450
    450
  • Thumbnail: Page 
451
    451
  • Thumbnail: Page 
452
    452
  • Thumbnail: Page 
453
    453
  • Thumbnail: Page 
454
    454
  • Thumbnail: Page 
455
    455
  • Thumbnail: Page 
456
    456
  • Thumbnail: Page 
457
    457