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Counting as integration in feasible analysis
Author(s) -
Ferreira Fernando,
Ferreira Gilda
Publication year - 2006
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200510035
Subject(s) - computability , base (topology) , mathematics , mathematical economics , reflection (computer programming) , calculus (dental) , epistemology , computer science , discrete mathematics , programming language , philosophy , mathematical analysis , medicine , dentistry
Suppose that it is possible to integrate real functions over a weak base theory related to polynomial time computability. Does it follow that we can count? The answer seems to be: obviously yes! We try to convince the reader that the severe restrictions on induction in feasible theories preclude a straightforward answer. Nevertheless, a more sophisticated reflection does indeed show that the answer is affirmative. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)