Titlebook: Notes on Set Theory; Yiannis N. Moschovakis Textbook 19941st edition Springer Science+Business Media New York 1994 Finite.Mathematica.axio

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https://doi.org/10.1007/978-1-4757-4153-7Finite; Mathematica; axiom of choice; language; mathematics; object; ordinal; recursion; set; set theory; sets

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Equinumerosity,After these preliminaries, we can formulate the fundamental definitions of Cantor about the size or cardinality of sets.

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Are Sets All There is?,tal theorem . of Cantor is about the set ? of real numbers, etc. Put another way, the results of Chapter 2 are not only about sets, but about points, numbers, functions, Cartesian products and many other mathematical objects which are plainly not sets. Where will we find these objects in the axioms of Zermelo which speak only about sets?

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Replacement and Other Axioms,set construction no less plausible than any of the constructive axioms (.) – (.) but powerful in its consequences. We will also introduce and discuss some additional principles which are often included in axiomatizations of set theory.

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