A new conservation result of WKL0 over RCA0

Abstract.

In this paper we give a partial answer to a conjecture of Tanaka. We prove that: if WKL₀ proves a sentence of the form (∀X)(∃!Y)ψ(X, Y) for a Σ⁰ ₃-formula ψ, then so does RCA₀.

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1. Instituto Superior Técnico, Dep. de Matemática, Av. Rovisco Pais, 1, 1096 Lisboa Codex, Portugal. e-mail: amfernandes@netcabo.pt, , , , , , PT

   António Marques Fernandes

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1. António Marques Fernandes
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Received: 12 April 1999 / Published online: 3 October 2001

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Fernandes, A. A new conservation result of WKL0 over RCA0. Arch. Math. Logic 41, 55–63 (2002). https://doi.org/10.1007/s001530200004

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• Issue Date: January 2002

• DOI: https://doi.org/10.1007/s001530200004

Keywords

• Partial Answer
• Conservation Result