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

Maximal Contiguous Degrees

Peter Cholak, Rod Downey and Stephen Walk
The Journal of Symbolic Logic
Vol. 67, No. 1 (Mar., 2002), pp. 409-437
Stable URL: http://www.jstor.org/stable/2695018
Page Count: 29
  • Download PDF
  • Cite this Item

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
Maximal Contiguous Degrees
Preview not available

Abstract

A computably enumerable (c.e.) degree is a maximal contiguous degree if it is contiguous and no c.e. degree strictly above it is contiguous. We show that there are infinitely many maximal contiguous degrees. Since the contiguous degrees are definable, the class of maximal contiguous degrees provides the first example of a definable infinite anti-chain in the c.e. degrees. In addition, we show that the class of maximal contiguous degrees forms an automorphism base for the c.e. degrees and therefore for the Turing degrees in general. Finally we note that the construction of a maximal contiguous degree can be modified to answer a question of Walk about the array computable degrees and a question of Li about isolated formulas.

Page Thumbnails

  • Thumbnail: Page 
409
    409
  • Thumbnail: Page 
410
    410
  • Thumbnail: Page 
411
    411
  • Thumbnail: Page 
412
    412
  • Thumbnail: Page 
413
    413
  • Thumbnail: Page 
414
    414
  • Thumbnail: Page 
415
    415
  • Thumbnail: Page 
416
    416
  • Thumbnail: Page 
417
    417
  • Thumbnail: Page 
418
    418
  • Thumbnail: Page 
419
    419
  • Thumbnail: Page 
420
    420
  • Thumbnail: Page 
421
    421
  • Thumbnail: Page 
422
    422
  • Thumbnail: Page 
423
    423
  • Thumbnail: Page 
424
    424
  • Thumbnail: Page 
425
    425
  • Thumbnail: Page 
426
    426
  • Thumbnail: Page 
427
    427
  • Thumbnail: Page 
428
    428
  • Thumbnail: Page 
429
    429
  • Thumbnail: Page 
430
    430
  • Thumbnail: Page 
431
    431
  • Thumbnail: Page 
432
    432
  • Thumbnail: Page 
433
    433
  • Thumbnail: Page 
434
    434
  • Thumbnail: Page 
435
    435
  • Thumbnail: Page 
436
    436
  • Thumbnail: Page 
437
    437