Classical provability of uniform versions and intuitionistic provability

Makoto Fujiwara, Ulrich Kohlenbach

Research output: Contribution to journalArticle

Abstract

Along the line of Hirst-Mummert and Dorais , we analyze the relationship between the classical provability of uniform versions Uni(S) of Π2-statements S with respect to higher order reverse mathematics and the intuitionistic provability of S. Our main theorem states that (in particular) for every Π2-statement S of some syntactical form, if its uniform version derives the uniform variant of ACA over a classical system of arithmetic in all finite types with weak extensionality, then S is not provable in strong semi-intuitionistic systems including bar induction BI in all finite types but also nonconstructive principles such as Konig's lemma KL and uniform weak Konig's lemma UWKL. Our result is applicable to many mathematical principles whose sequential versions imply ACA.

Original languageEnglish
Pages (from-to)132-150
Number of pages19
JournalMathematical Logic Quarterly
Volume61
Issue number3
DOIs
Publication statusPublished - 2015 May 1
Externally publishedYes

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Finite Type
Lemma
Reverse Mathematics
Proof by induction
Higher Order
Imply
Line
Theorem
Syntax
Form
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ASJC Scopus subject areas

  • Logic

Cite this

Classical provability of uniform versions and intuitionistic provability. / Fujiwara, Makoto; Kohlenbach, Ulrich.

In: Mathematical Logic Quarterly, Vol. 61, No. 3, 01.05.2015, p. 132-150.

Research output: Contribution to journalArticle

Fujiwara, Makoto ; Kohlenbach, Ulrich. / Classical provability of uniform versions and intuitionistic provability. In: Mathematical Logic Quarterly. 2015 ; Vol. 61, No. 3. pp. 132-150.
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