Kazuyuki TANAKA【田中 一之】, Professor Emeritus

Research Field

Logic and Foundations of Mathematics


Research Interests

 My research interests are logic and foundations of mathematics, specifically computability theory and reverse mathematics. Computability theory is a big branch of mathematical logic, originated with two geniuses Goedel and Turing, in which one endeavors to stratify the sets of natural numbers by way of relative computability. Reverse mathematics is a foundational study whose aim is to determine which axioms are necessary and sufficient to prove theorems of ordinary mathematics. These two fields share many ideas and techniques, and recently they have been developed together for mutual harmony.


Advice for the graduate study

 Only few universities in Japan provide proper undergraduate courses on mathematical logic. Thus, special knowledge of logic is not formally presupposed to enter our graduate program. However, it is indeed very difficult for an ill-prepared student to complete a master thesis within two years or so. So, if you are interested to study logic with me at Tohoku, you are strongly advised to consult me or other professional logicians as soon as possible. Be prepared and have no regrets.


Master's Thesis and Doctoral Dissertation Supervision

Model theory of Peano arithmetic, Formal systems of polynomial-time computable functions, Proof theory of real closed fields, Infinite games and inductive definitions, Nonstandard analysis and second order arithmetic, Algorithmic randomness, and many others.


Remarks

Personal Web Page Kazuyuki TANAKA
Laboratory Mathematics Building 508
Telephone  
E-mail tanaka.math[at]tohoku.ac.jp

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