2012 Fiscal Year Final Research Report
Proof-theoretic investigations on set theories
| Project/Area Number |
20340020
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Chiba University (2009-2012)
Kobe University (2008) |
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Principal Investigator |
TOSHIYASU Arai 千葉大学, 大学院・理学研究科, 教授 (40193049)
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| Project Period (FY) |
2008 – 2012
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| Keywords | 数学基礎論 / 証明の長さ / 集合論の証明論 |
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| Research Abstract |
I have primarily concerned with proof-theoretic investigations of axioms in set theories. Set theory is the basis of mathematics, and I have investigated proofs in set theory in terms of iterations: the number of iterations and operations. The axiom in set theory is a collection of propositions which are supposed to hold on sets. On the other side proving propositions is an indispensable action in mathematics including set theory. I have acquired knowledge of such foundational objects.
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Research Products
(36 results)
