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A Note on Goodman's Theorem

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Abstract

Goodman's theorem states that intuitionistic arithmetic in all finite types plus full choice, HAω + AC, is conservative over first-order intuitionistic arithmetic HA. We show that this result does not extend to various subsystems of HAω, HA with restricted induction.

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Authors and Affiliations

  1. Department of Computer Science, University of Aarhus, Ny Munkegade 540, DK-8000, Aarhus C, Denmark

    Ulrich Kohlenbach

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  1. Ulrich Kohlenbach
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Kohlenbach, U. A Note on Goodman's Theorem. Studia Logica 63, 1–5 (1999). https://doi.org/10.1023/A:1005278215757

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