Search results
Results from the WOW.Com Content Network
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 ...
It develops some basic model theory (rather specifically aimed at models of set theory) and the theory of Gödel's constructible universe L. The book then proceeds to describe the method of forcing. Kunen completely rewrote the book for the 2011 edition (under the title "Set Theory"), including more model theory.
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.
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.
In the language of set theory, atomic formulas are of the form x = y or x ∈ y, standing for equality and set membership predicates, respectively. The first level of the Lévy hierarchy is defined as containing only formulas with no unbounded quantifiers and is denoted by Δ 0 = Σ 0 = Π 0 {\displaystyle \Delta _{0}=\Sigma _{0}=\Pi _{0}} . [ 1 ]
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.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces the notion of class, which is a collection of sets defined by a formula whose quantifiers range only over sets.