Gaisi Takeuti
Encyclopedia
is a Japan
ese 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 is the current president (since 2003) of the Kurt Gödel Society, having worked on the respected 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.
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
ese mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, known for his work in proof theory
Proof theory
Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed...
.
After graduating from Tokyo University, he went to Princeton
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
to study under Kurt Gödel
Kurt Gödel
Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...
.
He later became a professor at the University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign
The University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...
. Takeuti is the current president (since 2003) of the Kurt Gödel Society, having worked on the respected 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
Takeuti conjecture
Takeuti's conjecture is the conjecture of Gaisi Takeuti that a sequent formalisation of second-order logic has cut-elimination . It was settled positively:...
speculates that a sequent
Sequent calculus
In proof theory and mathematical logic, sequent calculus is a family of formal systems sharing a certain style of inference and certain formal properties. The first sequent calculi, systems LK and LJ, were introduced by Gerhard Gentzen in 1934 as a tool for studying natural deduction in...
formalisation of second-order logic
Second-order logic
In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory....
has cut-elimination
Cut-elimination theorem
The cut-elimination theorem is the central result establishing the significance of the sequent calculus. It was originally proved by Gerhard Gentzen 1934 in his landmark paper "Investigations in Logical Deduction" for the systems LJ and LK formalising intuitionistic and classical logic respectively...
.
He is also known for his work on ordinal diagrams
Ordinal notation
In mathematical logic and set theory, an ordinal notation is a finite sequence of symbols from a finite alphabet which names an ordinal number according to some scheme which gives meaning to the language....
with Akiko Kino.