Counting as integration in feasible analysis | Zendy

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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)

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