The Euclidean Arithmetic developed by John Penn Mayberry in his book " The Foundations of Mathematics in the Theory of Sets " . also falls into the Aristotelian realist tradition.
12.
An earlier attempt in the post-war era to create a theory of sets where set membership is a matter of degree was made by Abraham Kaplan and Hermann Schott in 1951.
13.
It was during this time that Henney wrote her dissertation " The theory of set-valued additive functions defined on base-cones in Banach spaces with values in the collection of compact, convex sets ".
14.
One of the most cited versions of this definition is due to Kuratowski ( see below ) and his definition was used in the second edition of Bourbaki's " Theory of Sets ", published in 1970.
15.
With this contribution of von Neumann, the axiomatic system of the theory of sets avoided the contradictions of earlier systems, and became usable as a foundation for mathematics, despite the lack of a proof of its consistency.
16.
Erdoes, a member of the Royal Society and the academies of Hungary, Netherlands, United States, Australia, and India was especially noted for his work in numbers theory, theory of sets, probability theory and a host of other specialist problems.
17.
This situation is analogous to the treatments of theories of sets and minimal objects while proper classes are maximal objects by the membership relation ( which, of course, is not an order relation, so this analogy is not to be taken literally ).
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