Abstract
The goal in this first section is to become acquainted with logical notation and most of the axioms of Zermelo—Fraenkel set theory. We will also show how a few very important mathematical objects such as functions and relations can be formed from sets. Just as we have chosen to build mathematics using set theory, we will build set theory using logic.
The most distinct and beautiful statements of any truth must take at last the mathematical form. We might so simplify the rules of moral philosophy, as well as of arithmetic, that one formula would express them both.
H. D. Thoreau
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Henle, J.M. (1986). Logic and Set Theory. In: An Outline of Set Theory. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8680-3_2
Download citation
DOI: https://doi.org/10.1007/978-1-4613-8680-3_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96368-6
Online ISBN: 978-1-4613-8680-3
eBook Packages: Springer Book Archive