### Abstract

Along the line of Hirst-Mummert and Dorais , we analyze the relationship between the classical provability of uniform versions Uni(S) of Π_{2}-statements S with respect to higher order reverse mathematics and the intuitionistic provability of S. Our main theorem states that (in particular) for every Π_{2}-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 language | English |
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Pages (from-to) | 132-150 |

Number of pages | 19 |

Journal | Mathematical Logic Quarterly |

Volume | 61 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2015 May 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Logic

### Cite this

*Mathematical Logic Quarterly*,

*61*(3), 132-150. https://doi.org/10.1002/malq.201300056

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

Research output: Contribution to journal › Article

*Mathematical Logic Quarterly*, vol. 61, no. 3, pp. 132-150. https://doi.org/10.1002/malq.201300056

}

TY - JOUR

T1 - Classical provability of uniform versions and intuitionistic provability

AU - Fujiwara, Makoto

AU - Kohlenbach, Ulrich

PY - 2015/5/1

Y1 - 2015/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84929664147&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929664147&partnerID=8YFLogxK

U2 - 10.1002/malq.201300056

DO - 10.1002/malq.201300056

M3 - Article

VL - 61

SP - 132

EP - 150

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

SN - 0942-5616

IS - 3

ER -