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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.
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.
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.
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
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.
Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. [3] Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language.
This category is for the foundational concepts of naive set theory, in terms of which contemporary mathematics is typically expressed. Subcategories This category has the following 5 subcategories, out of 5 total.