caa a22 4500 469126752 CHVBK 20180323133152.0 cr unu---uuuuu 170328e19920701xx s 000 0 eng 10.1007/BF01794980 doi (NATIONALLICENCE)springer-10.1007/BF01794980 Kohlenbach Ulrich Fachbereich Mathematik, J. W. Goethe-Universität, Robert-Mayer-Strasse 6-10, W-6000, Frankfurt am Main, Federal Republic of Germany aut Pointwise hereditary majorization and some applications [Elektronische Daten] [Ulrich Kohlenbach] A pointwise version of the Howard-Bezem notion of hereditary majorization is introduced which has various advantages, and its relation to the usual notion of majorization is discussed. This pointwise majorization of primitive recursive functionals (in the sense of Gödel'sT as well as Kleene/Feferman's ) is applied to systems of intuitionistic and classical arithmetic (H andH c) in all finite types with full induction as well as to the corresponding systems with restricted inductionĤ↾ andĤ↾c. 1) H and Ĥ↾ are closed under a generalized fan-rule. For a restricted class of formulae this also holds forH c andĤ↾c. 2) We give a new and very perspicuous proof that for each one can construct a functional such that $$\tilde \Phi \alpha $$ is a modulus of uniform continuity for Φ on {β1∣∧n(βn≦αn)}. Such a modulus can also be obtained by majorizing any modulus of pointwise continuity for Φ. 3) The type structure ℳ of all pointwise majorizable set-theoretical functionals of finite type is used to give a short proof that quantifier-free "choice” with uniqueness (AC!)1,0-qf. is not provable within classical arithmetic in all finite types plus comprehension [given by the schema (C)ϱ:∨y 0ϱ∧x ϱ(yx=0⇔A(x)) for arbitraryA], dependent ω-choice and bounded choice. Furthermore ℳ separates several μ-operators. Springer-Verlag, 1992 Archive for Mathematical Logic Springer-Verlag 31/4(1992-07-01), 227-241 0933-5846 31:4<227 1992 31 153 https://doi.org/10.1007/BF01794980 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01794980 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kohlenbach Ulrich Fachbereich Mathematik, J. W. Goethe-Universität, Robert-Mayer-Strasse 6-10, W-6000, Frankfurt am Main, Federal Republic of Germany aut NATIONALLICENCE 773 0- Archive for Mathematical Logic Springer-Verlag 31/4(1992-07-01), 227-241 0933-5846 31:4<227 1992 31 153 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer