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.
a wonderful new book . . . Potter has written the best philosophical introduction to set theory on the market * Timothy Bays, Notre Dame Philosophical Reviews *
3: The hierarchy
4: The theory of sets
9: Real numbers
III. Cardinals and Ordinals
11: Basic cardinal arithmetic
13: Ordinal aritmetic
IV. Further axioms
14: Orders of infinity
15: The axiom of choice
16: Further cardinal arithmetic