1.  26
    Which Set Existence Axioms Are Needed to Prove the Separable Hahn-Banach Theorem?Douglas K. Brown & Stephen G. Simpson - 1986 - Annals of Pure and Applied Logic 31:123-144.
  2.  37
    The Baire Category Theorem in Weak Subsystems of Second-Order Arithmetic.Douglas K. Brown & Stephen G. Simpson - 1993 - Journal of Symbolic Logic 58 (2):557-578.
    Working within weak subsystems of second-order arithmetic Z2 we consider two versions of the Baire Category theorem which are not equivalent over the base system RCA0. We show that one version (B.C.T.I) is provable in RCA0 while the second version (B.C.T.II) requires a stronger system. We introduce two new subsystems of Z2, which we call RCA+ 0 and WKL+ 0, and show that RCA+ 0 suffices to prove B.C.T.II. Some model theory of WKL+ 0 and its importance in view of (...)
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  3.  19
    Vitali's Theorem and WWKL.Douglas K. Brown, Mariagnese Giusto & Stephen G. Simpson - 2002 - Archive for Mathematical Logic 41 (2):191-206.