Gaisi Takeuti (original) (raw)

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Gaisi Takeuti (竹内 外史, Takeuchi, Gaishi, January 25, 1926 – May 10, 2017) was a Japanese mathematician, known for his work in proof theory. After graduating from Tokyo University, he went to Princeton to study under Kurt Gödel. He later became a professor at the University of Illinois at Urbana–Champaign. Takeuti was president (2003–2009) of the Kurt Gödel Society, having worked on the book Memoirs of a Proof Theorist: Godel and Other Logicians. His goal was to prove the consistency of the real numbers. To this end, Takeuti's conjecture speculates that a sequent formalisation of second-order logic has cut-elimination. He is also known for his work on ordinal diagrams with Akiko Kino.

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dbo:abstract Takeuti Gaisi (jap. 竹内 外史, Takeuchi Gaishi; * 25. Januar 1926 in , Präfektur Ishikawa, Japan; † 10. Mai 2017) war ein japanischer mathematischer Logiker, bekannt für Beiträge zur Beweistheorie. Takeuti wurde 1956 an der Universität Tokio in mathematischer Logik promoviert. Er war ab 1950 zuerst Assistenzprofessor, später Professor an der Pädagogischen Universität Tokio und ab 1966 Professor an der University of Illinois at Urbana-Champaign. 1996 wurde er emeritiert. Takeutis Ziel in den 1950er Jahren war es, Widerspruchsfreiheitsbeweise für formale Systeme zu gewinnen, die die Analysis umfassen. Hierzu entwickelte er Methoden von Gerhard Gentzen weiter (unter anderem führte er ordinal diagrams ein). Takeuti gelang 1967 der Widerspruchsfreiheitsbeweis der Analysis (der Teil der Analysis, in der die Komprehension auf beliebige Formeln mit höchstens einem Mengenquantor eingeschränkt ist). Das war nach Kurt Schütte der erste Widerspruchsfreiheitsbeweis eines wesentlich imprädikativen Teils der Mathematik und Analysis. Takeutis Vermutung von 1953 besagt, dass im Logikkalkül endlicher Stufe die Schnittregel gilt (siehe Gentzenscher Hauptsatz). Sie wurde für das Kalkül 2. Stufe von William W. Tait (1966) und Dag Prawitz (1967, für höhere Ordnung 1969) bewiesen und unabhängig von Takahashi Motoo (1967, auch höhere Ordnung) und Jean-Yves Girard bewiesen. Von Takeuti stammten zwei Lehrbücher und Standardwerke, eines zur Beweistheorie und eines zur axiomatischen Mengenlehre. Anfang der 1950er Jahre befasste er sich auch mit Homotopietheorie und Knotentheorie (er hielt 1952/53 ein Seminar ab, das sein Doktorand besuchte). 1959/60, 1966 bis 1968 und 1971 bis 1972 war er am Institute for Advanced Study bei Kurt Gödel. 2003 bis 2009 war er Präsident der Kurt Gödel Society. 1998 erhielt er die tschechische Bolzano-Medaille und er erhielt den Okawa Preis für Veröffentlichungen. 1982 erhielt er den Asahi-Preis. (de) Gaisi Takeuti (竹内 外史, Takeuchi, Gaishi, January 25, 1926 – May 10, 2017) was a Japanese mathematician, known for his work in proof theory. After graduating from Tokyo University, he went to Princeton to study under Kurt Gödel. He later became a professor at the University of Illinois at Urbana–Champaign. Takeuti was president (2003–2009) of the Kurt Gödel Society, having worked on the book Memoirs of a Proof Theorist: Godel and Other Logicians. His goal was to prove the consistency of the real numbers. To this end, Takeuti's conjecture speculates that a sequent formalisation of second-order logic has cut-elimination. He is also known for his work on ordinal diagrams with Akiko Kino. (en) Gaisi Takeuti (竹内 外史 Takeuchi Gaishi, 25 de enero de 1926-10 de mayo de 2017) fue un matemático japonés conocido por su trabajo en la teoría de la demostración, que publicó al menos 47 trabajos en 263 publicaciones.​ Después de graduarse en la Universidad de Tokio, fue a la Universidad de Princeton donde estudió bajo la supervisión de Kurt Gödel. Posteriormente, se convertiría en profesor de la Universidad de Illinois en . El profesor Tauketi fue presidente, entre los años 2003 al 2009, de la ;​ durante su presidencia en dicha institución trabajó en el reconocido libro .​ Su principal meta académica fue probar la consistencia de los números reales para lo cual, el profesor Takeuti, especulaba que la formalización de una secuencia lógica de segundo orden se elimina.​ También fue conocido por su trabajo en los con . (es) 다케우치 가이시(일본어: 竹内 外史, 1926년 1월 25일 ~ 2017년 5월 10일)는 일본의 수리논리학자이다. 주 연구 분야는 증명 이론이다. 도쿄 대학을 졸업하고 쿠르트 괴델의 지도 하에 프린스턴 대학교에서 공부하였으며, 나중에는 일리노이 대학교 어배너-섐페인의 교수가 되었다. 다케우치는 2003년부터 2009년까지 쿠르트 괴델 협회(Kurt Gödel Society)의 회장을 맡고 있으면서, 유명한 책 《어떤 증명이론가의 회고록(Memoirs of a Proof Theorist: Gödel and Other Logicians)》을 쓰기도 했다. 다케우치의 목표는 실수 체계의 무모순성을 증명하는 것이다. 이를 위해 추측한 것으로 이 있는데, 의 시퀀트 공식화가 컷-제거 성질을 갖는다는 내용이다. 다케우치는 와 함께 한 (ordinal diagram)의 연구로도 유명하다. (ko) 竹内 外史（たけうち がいし、1926年1月25日 - 2017年5月10日）は、日本の数学者、論理学者。専門は数学基礎論（数理論理学・公理的集合論、証明論など）。イリノイ大学名誉教授。 解析学の基礎付けなど、数学基礎論の研究で世界的に知られる。昭和57年（1982年）朝日賞(昭和56年度)受賞。主な著作に「集合とはなにか」「現代集合論入門」「証明論と計算量」「層・圏・トポス」など。1966年以来、長くイリノイ大学で教鞭を執っていた。その間、の無矛盾性の証明を試みる。 (ja) Gaisi Takeuti (竹内 外史 Takeuchi Gaishi?, 25 de janeiro de 1926 – 10 de maio de 2017) foi um matemático japonês. É conhecido por seu trabalho sobre teoria da prova. Após a graduação na Universidade de Tóquio foi para a Universidade de Princeton, onde foi aluno de Kurt Gödel. Tornou-se depois professor da Universidade de Illinois em Urbana-Champaign. Takeuti foi presidente (2003-2009) da Sociedade Kurt Gödel, coautor do livro . Sua meta de pesquisas foi provar a consistência dos números reais. Com este propósito, a especula que uma formalização de lógica de segunda ordem tem eliminação de corte. (pt)
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rdfs:comment Gaisi Takeuti (竹内 外史, Takeuchi, Gaishi, January 25, 1926 – May 10, 2017) was a Japanese mathematician, known for his work in proof theory. After graduating from Tokyo University, he went to Princeton to study under Kurt Gödel. He later became a professor at the University of Illinois at Urbana–Champaign. Takeuti was president (2003–2009) of the Kurt Gödel Society, having worked on the book Memoirs of a Proof Theorist: Godel and Other Logicians. His goal was to prove the consistency of the real numbers. To this end, Takeuti's conjecture speculates that a sequent formalisation of second-order logic has cut-elimination. He is also known for his work on ordinal diagrams with Akiko Kino. (en) 다케우치 가이시(일본어: 竹内 外史, 1926년 1월 25일 ~ 2017년 5월 10일)는 일본의 수리논리학자이다. 주 연구 분야는 증명 이론이다. 도쿄 대학을 졸업하고 쿠르트 괴델의 지도 하에 프린스턴 대학교에서 공부하였으며, 나중에는 일리노이 대학교 어배너-섐페인의 교수가 되었다. 다케우치는 2003년부터 2009년까지 쿠르트 괴델 협회(Kurt Gödel Society)의 회장을 맡고 있으면서, 유명한 책 《어떤 증명이론가의 회고록(Memoirs of a Proof Theorist: Gödel and Other Logicians)》을 쓰기도 했다. 다케우치의 목표는 실수 체계의 무모순성을 증명하는 것이다. 이를 위해 추측한 것으로 이 있는데, 의 시퀀트 공식화가 컷-제거 성질을 갖는다는 내용이다. 다케우치는 와 함께 한 (ordinal diagram)의 연구로도 유명하다. (ko) 竹内 外史（たけうち がいし、1926年1月25日 - 2017年5月10日）は、日本の数学者、論理学者。専門は数学基礎論（数理論理学・公理的集合論、証明論など）。イリノイ大学名誉教授。 解析学の基礎付けなど、数学基礎論の研究で世界的に知られる。昭和57年（1982年）朝日賞(昭和56年度)受賞。主な著作に「集合とはなにか」「現代集合論入門」「証明論と計算量」「層・圏・トポス」など。1966年以来、長くイリノイ大学で教鞭を執っていた。その間、の無矛盾性の証明を試みる。 (ja) Gaisi Takeuti (竹内 外史 Takeuchi Gaishi?, 25 de janeiro de 1926 – 10 de maio de 2017) foi um matemático japonês. É conhecido por seu trabalho sobre teoria da prova. Após a graduação na Universidade de Tóquio foi para a Universidade de Princeton, onde foi aluno de Kurt Gödel. Tornou-se depois professor da Universidade de Illinois em Urbana-Champaign. Takeuti foi presidente (2003-2009) da Sociedade Kurt Gödel, coautor do livro . Sua meta de pesquisas foi provar a consistência dos números reais. Com este propósito, a especula que uma formalização de lógica de segunda ordem tem eliminação de corte. (pt) Takeuti Gaisi (jap. 竹内 外史, Takeuchi Gaishi; * 25. Januar 1926 in , Präfektur Ishikawa, Japan; † 10. Mai 2017) war ein japanischer mathematischer Logiker, bekannt für Beiträge zur Beweistheorie. Takeuti wurde 1956 an der Universität Tokio in mathematischer Logik promoviert. Er war ab 1950 zuerst Assistenzprofessor, später Professor an der Pädagogischen Universität Tokio und ab 1966 Professor an der University of Illinois at Urbana-Champaign. 1996 wurde er emeritiert. Von Takeuti stammten zwei Lehrbücher und Standardwerke, eines zur Beweistheorie und eines zur axiomatischen Mengenlehre. (de) Gaisi Takeuti (竹内 外史 Takeuchi Gaishi, 25 de enero de 1926-10 de mayo de 2017) fue un matemático japonés conocido por su trabajo en la teoría de la demostración, que publicó al menos 47 trabajos en 263 publicaciones.​ Después de graduarse en la Universidad de Tokio, fue a la Universidad de Princeton donde estudió bajo la supervisión de Kurt Gödel. Posteriormente, se convertiría en profesor de la Universidad de Illinois en . El profesor Tauketi fue presidente, entre los años 2003 al 2009, de la ;​ durante su presidencia en dicha institución trabajó en el reconocido libro .​ (es)
rdfs:label Takeuti Gaisi (de) Gaisi Takeuti (en) Gaisi Takeuti (es) 다케우치 가이시 (ko) 竹内外史 (ja) Gaisi Takeuti (pt)
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