Classical provability of uniform versions and intuitionistic provability

Makoto Fujiwara*, Ulrich Kohlenbach

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number3
Publication statusPublished - 2015 May 1
Externally publishedYes

ASJC Scopus subject areas

  • Logic


Dive into the research topics of 'Classical provability of uniform versions and intuitionistic provability'. Together they form a unique fingerprint.

Cite this