On the consistency proofs

• ARAI Toshiyasu

  Graduate School of Science and Technology, Kobe University

Bibliographic Information

Other Title

• 無矛盾性証明について
• ムムジュンセイ ショウメイ ニ ツイテ

Abstract

D. Hilbert raised the problem to prove consistency of formalized mathematics. In this paper I will expound its background and the status quo of the consistency proofs. First let me explain the intended significance of proving consistency, and a background idea to divide mathematical objects in two, i. e., transfinite/finitary objects. Next I will discuss impacts of the incompleteness theorems to the problem and their interpretation. Finally let me give sketches of the practice of the consistency proofs due to G. Gentzen et al. and their significance, and the present state of the consistency proofs.

Journal

• Journal of the Japan Association for Philosophy of Science

  Journal of the Japan Association for Philosophy of Science 34 (2), 91-99, 2007

  Japan Association for Philosophy of Science

Details

• CRID: 1390001205323753856
• NII Article ID: 10018919332
• NII Book ID: AN00036945
• DOI: 10.4288/kisoron1954.34.91
• ISSN: 18841236
• ISSN: 00227668
• NDL BIB ID: 8838171
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I8838171
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed