caa a22 4500 388038802 CHVBK 20180307125015.0 cr unu---uuuuu 161130e199812 xx s 000 0 eng 10.2307/2586648 doi S0022481200014237 pii (NATIONALLICENCE)cambridge-10.2307/2586648 Kohlenbach Ulrich Brics, Department of Computer Science, University of Århus, NYMunkegade, DK-8000 Århus C, Denmark. E-mail: kohlenb@brics.dk Relative constructivity [Elektronische Daten] [Ulrich Kohlenbach] In a previous paper [13] we introduced a hierarchy (G n A ω ) n∈ℕ of subsystems of classical arithmetic in all finite types where the growth of definable functions of G n A ω corresponds to the well-known Grzegorczyk hierarchy. Let AC-qf denote the schema of quantifier-free choice. [11], [13], [8] and [7] study various analytical principles Γ in the context of the theories GnA ω + AC-qf (mainly for n = 2) and use proof-theoretic tools like, e.g., monotone functional interpretation (which was introduced in [12]) to determine their impact on the growth of uniform bounds Φ such that which are extractable from given proofs (based on these principles Γ) of sentences Here A 0(u, k, v, w) is quantifier-free and contains only u, k, v, w as free variables; t is a closed term and ≤ p is defined pointwise. The term ‘uniform bound' refers to the fact that Φ does not depend on v ≤ p tuk (see [12] for the relevance of such uniform bounds in numerical analysis and for concrete applications to approximation theory). Copyright © Association for Symbolic Logic 1998 The Journal of Symbolic Logic Cambridge University Press 63/4(1998-12), 1218-1238 0022-4812 63:4<1218 1998 63 JSL https://doi.org/10.2307/2586648 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586648 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kohlenbach Ulrich Brics, Department of Computer Science, University of Århus, NYMunkegade, DK-8000 Århus C, Denmark. E-mail: kohlenb@brics.dk NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/4(1998-12), 1218-1238 0022-4812 63:4<1218 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge