## 抄録

The logical system P-W is an implicational non-commutative intuitionistic logic defined by axiom schemes B = (b → c) → (a → b) → a → c. B′ = (a → b) → (b → c) → a → c. I = a → a with the rules of modus ponens and substitution. The P-W problem is a problem asking whether α = β holds if α → β and β → α are both provable in P-W. The answer is affirmative. The first to prove this was E. P. Martin by a semantical method. In this paper, we give the first proof of Martin's theorem based on the theory of simply typed λ-calculus. This proof is obtained as a corollary to the main theorem of this paper, shown without using Martin's Theorem, that any closed hereditary right-maximal linear (HRML) λ-term of type α → α is βη-reducible to λx.x. Here the HRML λ-terms correspond, via the Curry-Howard isomorphism, to the P-W proofs in natural deduction style.

本文言語 | 英語 |
---|---|

ページ（範囲） | 1841-1849 |

ページ数 | 9 |

ジャーナル | Journal of Symbolic Logic |

巻 | 65 |

号 | 4 |

DOI | |

出版ステータス | 出版済み - 12 2000 |

## All Science Journal Classification (ASJC) codes

- 哲学
- 論理