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

The Π₃-Theory of the $\Sigma _{2}^{0}$ -Enumeration Degrees Is Undecidable

Thomas F. Kent
The Journal of Symbolic Logic
Vol. 71, No. 4 (Dec., 2006), pp. 1284-1302
Stable URL: http://www.jstor.org/stable/27588513
Page Count: 19
  • Read Online (Free)
  • Download ($10.00)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
The Π₃-Theory of the
          $\Sigma _{2}^{0}$
          -Enumeration Degrees Is Undecidable
Preview not available

Abstract

We show that in the language of {≤}, the Π₃-fragment of the first order theory of the $\Sigma _{2}^{0}$-enumeration degrees is undecidable. We then extend this result to show that the Π₃-theory of any substructure of the enumeration degrees which contains the $\Delta _{2}^{0}$-degrees is undecidable.

Page Thumbnails

  • Thumbnail: Page 
1284
    1284
  • Thumbnail: Page 
1285
    1285
  • Thumbnail: Page 
1286
    1286
  • Thumbnail: Page 
1287
    1287
  • Thumbnail: Page 
1288
    1288
  • Thumbnail: Page 
1289
    1289
  • Thumbnail: Page 
1290
    1290
  • Thumbnail: Page 
1291
    1291
  • Thumbnail: Page 
1292
    1292
  • Thumbnail: Page 
1293
    1293
  • Thumbnail: Page 
1294
    1294
  • Thumbnail: Page 
1295
    1295
  • Thumbnail: Page 
1296
    1296
  • Thumbnail: Page 
1297
    1297
  • Thumbnail: Page 
1298
    1298
  • Thumbnail: Page 
1299
    1299
  • Thumbnail: Page 
1300
    1300
  • Thumbnail: Page 
1301
    1301
  • Thumbnail: Page 
1302
    1302