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Gaisi Takeuti. 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's conjecture. In mathematics, Takeuti's conjecture is the conjecture of Gaisi Takeuti that a sequent formalisation of second-order logic has cut-elimination (Takeuti 1953). It was settled positively: Takeuti's conjecture is equivalent to the 1-consistency of second-order arithmetic in the sense that each of the statements can be derived ...
Proof theory is a major branch [ 1] of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed ...
In the mathematical fields of set theory and proof theory, the Takeuti–Feferman–Buchholz ordinal (TFBO) is a large countable ordinal, which acts as the limit of the range of Buchholz's psi function and Feferman's theta function. [ 1][ 2] It was named by David Madore, [ 2] after Gaisi Takeuti, Solomon Feferman and Wilfried Buchholz.
Large countable ordinal. In the mathematical discipline of set theory, there are many ways of describing specific countable ordinals. The smallest ones can be usefully and non-circularly expressed in terms of their Cantor normal forms. Beyond that, many ordinals of relevance to proof theory still have computable ordinal notations (see ordinal ...
Theories of iterated inductive definitions. In set theory and logic, Buchholz's ID hierarchy is a hierarchy of subsystems of first-order arithmetic. The systems/theories are referred to as "the formal theories of ν-times iterated inductive definitions". ID ν extends PA by ν iterated least fixed points of monotone operators.
Gaisi Takeuti. Proof theory. Volume 81 of Studies in Logic and the Foundation of Mathematics. North-Holland, Amsterdam, 1975. Anne Sjerp Troelstra and Helmut Schwichtenberg. Basic Proof Theory. Edition: 2, illustrated, revised. Published by Cambridge University Press, 2000.
Scientific career. Fields. Logic. Institutions. CNRS. Doctoral advisor. Jean-Louis Krivine [ fr] Jean-Yves Girard ( French: [ʒiʁaʁ]; born 1947) is a French logician working in proof theory. He is a research director ( emeritus) at the mathematical institute of University of Aix-Marseille, at Luminy .