Algebras of Sets and Combinatorics

Algebras of Sets and Combinatorics

English | 2002 | ISBN: 0821827650 | 256 Pages | PDF | 2,4 + 13,6 MB

An algebra $A$ on a set $X$ is a family of subsets of this set closed under the operations of union and difference of two subsets. The main topic of the book is the study of various algebras and families of algebras on an abstract set $X$. The author shows how this is related to famous problems by Lebesgue, Banach, and Ulam on the existence of certain measures on abstract sets, with corresponding algebras being algebras of measurable subsets with respect to these measures. In particular it is shown that for a certain algebra not to coincide with the algebra of all subsets of $X$ is equivalent to the existence of a nonmeasurable set with respect to a given measure. Although these questions don't seem to be related to mathematical logic, many results in this area were proved by ``metamathematical'' methods, using the method of forcing and other tools related to axiomatic set theory. However, in the present book, the author uses ``elementary'' (mainly combinatorial) methods to study properties of algebras on a set. Presenting new and original material, the book is written in a clear and readable style and illustrated by many examples and figures. The book will be useful to researchers and graduate students working in set theory, mathematical logic, and combinatorics.

Download:

http://longfiles.com/b49b8x9ciasj/Algebras_of_Sets_and_Combinatorics.pdf.html

[Fast Download] Algebras of Sets and Combinatorics


Ebooks related to "Algebras of Sets and Combinatorics" :
Excel 2016 for Educational and Psychological Statistics: A Guide to Solving Practical Problems
Quantitative Psychology Research: The 80th Annual Meeting of the Psychometric Society, Beijing, 2015
Kripke's Worlds: An Introduction to Modal Logics via Tableaux
Neuromathematics of Vision
Analysis: From Concepts to Applications
Introduction to Smooth Manifolds
Higher-Order Finite Element Methods
Metalogic: An Introduction to the Metatheory of Standard First Order Logic
Numerical Polynomial Algebra
Pseudo-periodic Maps and Degeneration of Riemann Surfaces
Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.