Philosophia Mathematica:nkz029 (forthcoming)

Authors
Neil Tennant
Ohio State University
Abstract
ABSTRACT The one-page 1978 informal proof of Goodman and Myhill is regimented in a weak constructive set theory in free logic. The decidability of identities in general is derived; then, of sentences in general. Martin-Löf’s and Bell’s receptions of the latter result are discussed. Regimentation reveals the form of Choice used in deriving Excluded Middle. It also reveals an abstraction principle that the proof employs. It will be argued that the Goodman–Myhill result does not provide the constructive set theorist with a dispositive reason for not adopting Choice.
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DOI 10.1093/philmat/nkz029
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References found in this work BETA

Elements of Intuitionism.Michael Dummett - 1977 - Oxford University Press.
Constructive Set Theory.John Myhill - 1975 - Journal of Symbolic Logic 40 (3):347-382.
A General Theory of Abstraction Operators.Neil Tennant - 2004 - Philosophical Quarterly 54 (214):105-133.
Choice Implies Excluded Middle.N. Goodman & J. Myhill - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (25-30):461-461.
Choice Implies Excluded Middle.N. Goodman & J. Myhill - 1978 - Mathematical Logic Quarterly 24 (25‐30):461-461.

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