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Archive for Mathematical Logic

, Volume 47, Issue 3, pp 205–210 | Cite as

Subsystems of second-order arithmetic between RCA0 and WKL0

  • Carl Mummert
Article

Abstract

We study the Lindenbaum algebra \({\fancyscript{A}}\) (WKL o, RCA o) of sentences in the language of second-order arithmetic that imply RCA o and are provable from WKL o. We explore the relationship between \({\Sigma^1_1}\) sentences in \({\fancyscript{A}}\) (WKL o, RCA o) and \({\Pi^0_1}\) classes of subsets of ω. By applying a result of Binns and Simpson (Arch. Math. Logic 43(3), 399–414, 2004) about \({\Pi^0_1}\) classes, we give a specific embedding of the free distributive lattice with countably many generators into \({\fancyscript{A}}\) (WKL o, RCA o).

Keywords

Reverse mathematics Medvedev reducibility Muchnik reducibility Second order arithmetic 

Mathematics Subject Classification (2000)

03B30 03F35 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Mathematical SciencesAppalachian State UniversityBooneUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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