7 found
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  1.  4
    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.
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  2.  22
    Algebraic Disguises ofΣ 1 0 Induction.Kostas Hatzikiriakou - 1989 - Archive for Mathematical Logic 29 (1):47-51.
  3.  12
    A Note on Ordinal Numbers and Rings of Formal Power Series.Kostas Hatzikiriakou - 1994 - Archive for Mathematical Logic 33 (4):261-263.
  4.  7
    WKL< Sub> 0 and Stone's Separation Theorem for Convex Sets.Kostas Hatzikiriakou - 1996 - Annals of Pure and Applied Logic 77 (3):245-249.
    The Stone's Separation Theorem is equivalent to Weak König's Lemma.
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  5.  7
    WKL0 and Stone's Separation Theorem for Convex Sets.Kostas Hatzikiriakou - 1996 - Annals of Pure and Applied Logic 77 (3):245-249.
    The Stone's Separation Theorem is equivalent to Weak König's Lemma.
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  6.  9
    Countable Valued Fields in Weak Subsystems of Second-Order Arithmetic.Kostas Hatzikiriakou & Stephen G. Simpson - 1989 - Annals of Pure and Applied Logic 41 (1):27-32.
  7.  3
    Minimal Prime Ideals and Arithmetic Comprehension.Kostas Hatzikiriakou - 1991 - Journal of Symbolic Logic 56 (1):67-70.