2013 Fiscal Year Final Research Report

Construction of an interpretation between systems of applicative theory and set theory

Research Project

Project/Area Number	24840022
Research Category	Grant-in-Aid for Research Activity Start-up
Allocation Type	Single-year Grants
Research Field	General mathematics (including Probability theory/Statistical mathematics)
Research Institution	Japan Advanced Institute of Science and Technology
Principal Investigator	TAKAKO Nemoto 北陸先端科学技術大学院大学, 情報科学研究科, 助教 (20546155)
Project Period (FY)	2012-08-31 – 2014-03-31
Keywords	集合論 / 演算適用の理論 / 証明論 / 翻訳 / 算術
Research Abstract	We gave an interpretation from set theory, whoes basic objects are sets, into applicative theory, whoes basic objects are operators and natural numbers, by modefing the interpretation method from set theory into type theory, proposed by P. Aczel. It turned out that set theories which can be interpreted by this new method is defferent from ordinal set theory in the following sense: 1. They allows the existtence of universal set, namely, the set of ALL set; 2. They does not allow rather weak set comperehension axioms. We have constructed an appropreate set theory which can be interpreted by this method in the sense of the proof theoretic strength.

(5 results)