Abstract
Several properties of monotone functionals (MF) and monotone majorizable functionals (MMF) used in the earlier work by the author and van de Pol are proved. It turns out that the terms of the simply typed lambda-calculus define MF, but adding primitive recursion, and even monotonic primitive recursion changes the situation: already λZ.Z(1 — sg) is not MMF. It is proved that extensionality is not Dialectica-realizable by MMF, and a simple example of a MF which is not hereditarily majorizable is given.
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Schwichtenberg, H. Monotone Majorizable Functionals. Studia Logica 62, 283–289 (1999). https://doi.org/10.1023/A:1026459821186
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DOI: https://doi.org/10.1023/A:1026459821186