A Note on Goodman's Theorem |
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| Authors: | Kohlenbach Ulrich |
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| Institution: | (1) Department of Computer Science, University of Aarhus, Ny Munkegade 540, DK-8000 Aarhus C, Denmark |
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| Abstract: | Goodman's theorem states that intuitionistic arithmetic in all finite types plus full choice, HA + AC, is conservative over first-order intuitionistic arithmetic HA. We show that this result does not extend to various subsystems of HA, HA with restricted induction. |
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| Keywords: | Goodman's theorem intuitionistic arithmetic axiom of choice restricted induction |
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