A note on Spector's quantifier-free rule of extensionality

Archive for Mathematical Logic 40 (2):89-92 (2001)
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Abstract

In this note we show that the so-called weakly extensional arithmetic in all finite types, which is based on a quantifier-free rule of extensionality due to C. Spector and which is of significance in the context of Gödel"s functional interpretation, does not satisfy the deduction theorem for additional axioms. This holds already for Π0 1-axioms. Previously, only the failure of the stronger deduction theorem for deductions from (possibly open) assumptions (with parameters kept fixed) was known

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10.1007/s001530000048

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Pointwise hereditary majorization and some applications.Ulrich Kohlenbach - 1992 - Archive for Mathematical Logic 31 (4):227-241.
Equivalence of bar recursors in the theory of functionals of finite type.Marc Bezem - 1988 - Archive for Mathematical Logic 27 (2):149-160.

Add more references