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Reforming Takeuti's Quantum Set Theory to Satisfy De Morgan's Laws [PDF]
Masanao Ozawa
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Mathematicians manipulate sets with confidence almost every day, rarely making mistakes. Few of us, however, could accurately quote what are often referred to as "the" axioms of set theory. This suggests that we all carry around with us, perhaps subconsciously, a reliable body of operating principles for manipulating sets.
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AbstractWe discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higher-order reflection principles.
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Basic Topological Concepts and a Construction of Real Numbers in Alternative Set Theory [PDF]
Kiri Sakahara, Takashi Sato
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Classical Set Theory: Theory of Sets and Classes
This is a short introductory course to Set Theory, based on axioms of von Neumann--Bernays--Gödel (briefly NBG). The text can be used as a base for a lecture course in Foundations of Mathematics, and contains a reasonable minimum which a good (post-graduate) student in Mathematics should know about foundations of this science.
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A credit risk evaluation based on intuitionistic fuzzy set theory for the sustainable development of electricity retailing companies in China [PDF]
Gejirifu De +5 more
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Partial identification using random set theory [PDF]
This paper illustrates how the use of random set theory can benefit partial identification analysis. We revisit the origins of Manski's work in partial identification (e.g., Manski (1989, 1990)), focusing our discussion on identification of probability ...
Arie Beresteanu +2 more
core
Combining Higher-Order Logic with Set Theory Formalizations. [PDF]
Kaliszyk C, Pąk K.
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