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Set Theory: An Introduction to Independence Proofs is a textbook and reference work in set theory by Kenneth Kunen. It starts from basic notions, including the ZFC axioms, and quickly develops combinatorial notions such as trees , Suslin's problem , , and Martin's axiom .
Von Neumann–Bernays–Gödel set theory (NBG) is a commonly used conservative extension of Zermelo–Fraenkel set theory that does allow explicit treatment of proper classes. There are many equivalent formulations of the axioms of Zermelo–Fraenkel set theory. Most of the axioms state the existence of particular sets defined from other sets.
First published in April 1914, Grundzüge der Mengenlehre was the first comprehensive introduction to set theory. In addition to the systematic treatment of known results in set theory, the book also contains chapters on measure theory and topology, which were then still considered parts of set theory. Hausdorff presented and developed original ...
Naive Set Theory is a mathematics textbook by Paul Halmos providing an undergraduate introduction to set theory. [1] Originally published by Van Nostrand in 1960, [ 2 ] it was reprinted in the Springer-Verlag Undergraduate Texts in Mathematics series in 1974.
It is the algebra of the set-theoretic operations of union, intersection and complementation, and the relations of equality and inclusion. For a basic introduction to sets see the article on sets, for a fuller account see naive set theory, and for a full rigorous axiomatic treatment see axiomatic set theory.
In set theory, the core model is a definable inner model of the universe of all sets. Even though set theorists refer to "the core model", it is not a uniquely identified mathematical object. Rather, it is a class of inner models that under the right set-theoretic assumptions have very special properties, most notably covering properties.
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The axioms of Zermelo set theory are stated for objects, some of which (but not necessarily all) are sets, and the remaining objects are urelements and not sets. Zermelo's language implicitly includes a membership relation ∈, an equality relation = (if it is not included in the underlying logic), and a unary predicate saying whether an object is a set.