The ∀∃-theory of the effectively closed Medvedev degrees is decidable

  • Joshua A. Cole
  • Takayuki KiharaEmail author


We show that there is a computable procedure which, given an ∀∃-sentence \({\varphi}\) in the language of the partially ordered sets with a top element 1 and a bottom element 0, computes whether \({\varphi}\) is true in the Medvedev degrees of \({\Pi^0_1}\) classes in Cantor space, sometimes denoted by \({\mathcal{P}_s}\) .


Recursion theory Medvedev degree \({\Pi^0_1}\) Class 

Mathematics Subject Classification (2000)



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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA
  2. 2.Mathematical InstituteTohoku UniversitySendai, MiyagiJapan

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