No CrossRef data available.
Article contents
ON CUPPING AND AHMAD PAIRS
Part of:
Computability and recursion theory
Published online by Cambridge University Press: 11 December 2022
Abstract
Working toward showing the decidability of the
$\forall \exists $
-theory of the
${\Sigma ^0_2}$
-enumeration degrees, we prove that no so-called Ahmad pair of
${\Sigma ^0_2}$
-enumeration degrees can join to
${\mathbf 0}_e'$
.
Keywords
MSC classification
- Type
- Article
- Information
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic
References
Ahmad, S.,
Some results on the structure of the
${\boldsymbol{\varSigma}}_{\boldsymbol{2}}$
enumeration degrees
, Ph.D. thesis, Simon Fraser University, Canada, 1989.Google Scholar
${\boldsymbol{\varSigma}}_{\boldsymbol{2}}$
enumeration degrees
, Ph.D. thesis, Simon Fraser University, Canada, 1989.Google ScholarAhmad, S. and Lachlan, A. H.,
Some special pairs of
${\varSigma}_2$
e-degrees
.
Mathematical Logic Quarterly
, vol. 44 (1998), no. 4, pp. 431–449.Google Scholar
${\varSigma}_2$
e-degrees
.
Mathematical Logic Quarterly
, vol. 44 (1998), no. 4, pp. 431–449.Google ScholarGanchev, H. A. and Soskova, M. I., Interpreting true arithmetic in the local structure of the enumeration degrees, this Journal, vol. 77 (2012), pp. 1184–1194.Google Scholar
Goh, J. L., Ng, K. M., Lempp, S., and Soskova, M. I., Extensions of two constructions of Ahmad.
Computability
, vol. 11 (2022), no. 3-4, pp. 269–297.Google Scholar
Goh, J. L., Ng, K. M., Lempp, S., and Soskova, M. I., Extensions of embeddings of 1-point extensions of finite antichains in the
${\varSigma}_2^0$
-enumeration degrees, in preparation.Google Scholar
${\varSigma}_2^0$
-enumeration degrees, in preparation.Google ScholarKent, T. F., The
${\varPi}_3$
-theory of the
${\varSigma}_2^0$
-enumeration degrees is undecidable, this Journal, vol. 71 (2006), pp. 1284–1302.Google Scholar
${\varPi}_3$
-theory of the
${\varSigma}_2^0$
-enumeration degrees is undecidable, this Journal, vol. 71 (2006), pp. 1284–1302.Google ScholarLempp, S., Lerman, M., and Reed Solomon, D.,
Embedding finite lattices into the computably enumerable degrees—A status survey
,
Logic Colloquium’02
(Z. Chatzidakis, P. Koepke and W. Pohlers, editors), Lecture Notes in Logic, vol. 27, Association for Symbolic Logic, La Jolla, 2006, pp. 206–229.Google Scholar
Lempp, S., Nies, A., and Slaman, T. A.,
The
${\varPi}_3$
-theory of the computably enumerable Turing degrees is undecidable
.
Transactions of the American Mathematical Society
, vol. 350 (1998), pp. 2719–2736.Google Scholar
${\varPi}_3$
-theory of the computably enumerable Turing degrees is undecidable
.
Transactions of the American Mathematical Society
, vol. 350 (1998), pp. 2719–2736.Google ScholarLempp, S., Slaman, T. A., and Sorbi, A.,
On extensions of embeddings into the enumeration degrees of the
${\varSigma}_2^0$
-sets
.
Journal of Mathematical Logic
, vol. 5 (2005), pp. 247–298.Google Scholar
${\varSigma}_2^0$
-sets
.
Journal of Mathematical Logic
, vol. 5 (2005), pp. 247–298.Google ScholarLempp, S. and Sorbi, A., Embedding finite lattices into the
${\varSigma}_2^0$
-enumeration degrees, this Journal, vol. 67 (2002), pp. 69–90.Google Scholar
${\varSigma}_2^0$
-enumeration degrees, this Journal, vol. 67 (2002), pp. 69–90.Google ScholarNies, A., Shore, R. A., and Slaman, T. A.,
Interpretability and definability in the recursively enumerable degrees
.
Proceedings of the London Mathematical Society (3)
, vol. 77 (1998), pp. 241–291.CrossRefGoogle Scholar
Sacks, G. E.,
On the degrees less than
${\boldsymbol{0}}^{\prime }.$
Annals of Mathematics. Second Series
, vol. 77 (1963), pp. 211–231.Google Scholar
${\boldsymbol{0}}^{\prime }.$
Annals of Mathematics. Second Series
, vol. 77 (1963), pp. 211–231.Google ScholarSlaman, T. A. and Woodin, W. H.,
Definability in the enumeration degrees
.
Archive for Mathematical Logic
, vol. 36 (1997), nos. 4–5, pp. 255–267.Google Scholar