Switch to: References

Add citations

You must login to add citations.
  1. Reverse mathematics, young diagrams, and the ascending chain condition.Kostas Hatzikiriakou & Stephen G. Simpson - 2017 - Journal of Symbolic Logic 82 (2):576-589.
    LetSbe the group of finitely supported permutations of a countably infinite set. Let$K[S]$be the group algebra ofSover a fieldKof characteristic 0. According to a theorem of Formanek and Lawrence,$K[S]$satisfies the ascending chain condition for two-sided ideals. We study the reverse mathematics of this theorem, proving its equivalence over$RC{A_0}$ to the statement that${\omega ^\omega }$is well ordered. Our equivalence proof proceeds via the statement that the Young diagrams form a well partial ordering.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • On the Uniform Computational Content of the Baire Category Theorem.Vasco Brattka, Matthew Hendtlass & Alexander P. Kreuzer - 2018 - Notre Dame Journal of Formal Logic 59 (4):605-636.
    We study the uniform computational content of different versions of the Baire category theorem in the Weihrauch lattice. The Baire category theorem can be seen as a pigeonhole principle that states that a complete metric space cannot be decomposed into countably many nowhere dense pieces. The Baire category theorem is an illuminating example of a theorem that can be used to demonstrate that one classical theorem can have several different computational interpretations. For one, we distinguish two different logical versions of (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Primitive recursive reverse mathematics.Nikolay Bazhenov, Marta Fiori-Carones, Lu Liu & Alexander Melnikov - 2024 - Annals of Pure and Applied Logic 175 (1):103354.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark