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Israel Journal of Mathematics

, Volume 196, Issue 1, pp 345–361 | Cite as

On the strength of the finite intersection principle

  • Damir D. Dzhafarov
  • Carl Mummert
Article

Abstract

We study the logical content of several maximality principles related to the finite intersection principle (FIP) in set theory. Classically, these are all equivalent to the axiom of choice, but in the context of reverse mathematics their strengths vary: some are equivalent to ACA0 over RCA0, while others are strictly weaker and incomparable with WKL0. We show that there is a computable instance of FIP every solution of which has hyperimmune degree, and that every computable instance has a solution in every nonzero c.e. degree. In particular, FIP implies the omitting partial types principle (OPT) over RCA0. We also show that, modulo Σ 2 0 induction, FIP lies strictly below the atomic model theorem (AMT).

Keywords

Intersection Property Initial Segment Force Notion Intersection Principle Logical Content 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University Magnes Press 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA
  2. 2.Department of MathematicsMarshall UniversityHuntingtonUSA

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