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  1. Countable Algebra and Set Existence Axioms.H. M. Friedman - 1983 - Annals of Pure and Applied Logic 25 (2):141.
  • 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 (2):123-144.
  • Which Set Existence Axioms Are Needed to Prove the Cauchy/Peano Theorem for Ordinary Differential Equations?Stephen G. Simpson - 1984 - Journal of Symbolic Logic 49 (3):783-802.
    We investigate the provability or nonprovability of certain ordinary mathematical theorems within certain weak subsystems of second order arithmetic. Specifically, we consider the Cauchy/Peano existence theorem for solutions of ordinary differential equations, in the context of the formal system RCA 0 whose principal axioms are ▵ 0 1 comprehension and Σ 0 1 induction. Our main result is that, over RCA 0 , the Cauchy/Peano Theorem is provably equivalent to weak Konig's lemma, i.e. the statement that every infinite {0, 1}-tree (...)
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