Michael Potter – Set Theory and Its Philosophy: A Critical Introduction

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart.
Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels.
What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Readership: Philosophy graduates and advanced undergraduates, who have a logical training and are progressing to advanced logic and/or philosophy of mathematics; those with a mathematical training who want to investigate the philosophy of their subject.

Table of Contents:

I. Sets
1: Logic
2: Collections
3: The hierarchy
4: The theory of sets
5: Classes
II. Numbers
6: Arithmetic
7: Counting
8: Lines
9: Real numbers
III. Cardinals and Ordinals
10: Cardinals
11: Basic cardinal arithmetic
12: Ordinals
13: Ordinal aritmetic
IV. Further axioms
14: Orders of infinity
15: The axiom of choice
16: Further cardinal arithmetic   źródło opisu: http://ukcatalogue.oup.com/product/9780199270415.do źródło okładki: http://ukcatalogue.oup.com/product/9780199270415.do