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Two General Results on Intuitionistic Bounded Theories
Author(s) -
Ferreira Fernando
Publication year - 1999
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.19990450310
Subject(s) - bounded function , mathematics , bounding overwatch , scheme (mathematics) , discrete mathematics , pure mathematics , algebra over a field , computer science , artificial intelligence , mathematical analysis
We study, within the framework of intuitionistic logic, two well‐known general results of (classical logic) bounded arithmetic. Firstly, Parikh's theorem on the existence of bounding terms for the provably total functions. Secondly, the result which states that adding the scheme of bounded collection to (suitable) bounded theories does not yield new II 2 consequences.