Israel Journal of Mathematics

, Volume 178, Issue 1, pp 229–252 | Cite as

The theory of the α degrees is undecidable

Article

Abstract

Let α be an arbitrary Σ1-admissible ordinal. For each n, there is a formula φn(\(\vec x,\vec y\)) such that for any relation R on a finite set F with n elements, there are α-degrees \({\vec p}\) such that the relation defined by φn(\(\vec x,\vec p\)) is isomorphic to R. Consequently, the theory of α-degrees is undecidable.

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Copyright information

© Hebrew University Magnes Press 2010

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceNational University of SingaporeSingaporeSingapore
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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