Gaisi Takeuti

Gaisi Takeuti
Gaisi Takeuti
竹内外史
Born	January 25, 1926
Died	May 10, 2017 (aged 91)
Nationality	Japanese
Education	Tokyo University
Alma mater	Princeton
Known for	Work in proof theory
	Scientific career
Fields	Mathematics
Institutions	University of Illinois at Urbana–Champaign

Gaisi Takeuti (竹内外史, Takeuchi, Gaishi, January 25, 1926 – May 10, 2017^[1]) was a Japanese mathematician, known for his work in proof theory.^[2]

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.^[3] He is also known for his work on ordinal diagrams with Akiko Kino.

Publications

Takeuti, Gaisi (1953). "On a generalized logic calculus". Japanese Journal of Mathematics. 23: 39–96. doi:10.4099/jjm1924.23.0_39. ISSN 0075-3432.
Takeuti, Gaisi (1954). "Errata to 'On a Generalized Logic Calculus'". Japanese Journal of Mathematics. 24: 149–156. doi:10.4099/jjm1924.24.0_149. ISSN 0075-3432.
Takeuti, Gaisi; Zaring, Wilson M. (2011) [1982], Introduction to axiomatic set theory, Graduate Texts in Mathematics, vol. 1 (2nd ed.), New York-Berlin: Springer-Verlag, doi:10.1007/978-1-4613-8168-6, ISBN 978-1-4613-8170-9, MR 0349390
Takeuti, Gaisi; Zaring, Wilson M. (1973), Axiomatic set theory, Graduate Texts in Mathematics, vol. 8, New York-Berlin: Springer-Verlag, doi:10.1007/978-1-4684-8751-0, ISBN 978-0-387-90050-6, MR 0416914 2013 Dover reprint
Takeuti, Gaisi (2013) [1975]. Proof theory (Second ed.). Mineola, New York: Dover Publications. ISBN 978-0-486-49073-1.
Takeuti, Gaisi (2015) [1978], Two applications of logic to mathematics, Publications of the Mathematical Society of Japan, vol. 13, Princeton, N.J.: Princeton University Press, ISBN 978-0-69-161022-1, MR 0505474
Takeuti, Gaisi (2003) [1998], Memoirs of a proof theorist. Gödel and other logicians, River Edge, NJ: World Scientific Publishing Co., Inc., ISBN 978-981-238-279-5, MR 1984952

Notes

^ Sam Buss (2017-05-10). "[Proof Complexity] Gaisi Takeuti". Proof-Complexity mailing list. Retrieved 2019-01-13.
^ Takeuti 2013.
^ Takeuti 1953. An erratum to this article was published in the same journal as (Takeuti 1954).