Ebook: Set Theory in Computer Science - A Gentle Introduction to Mathematical Modeling I

University of Illinois at Urbana-Champaign Urbana, IL 61801, USA, 2011. — 183 p.Table of Contents:
Motivation.
Set Theory as an Axiomatic Theory.
The Empty Set, Extensionality, and Separation.
Pairing, Unions, Powersets, and Infinity.
Case Study: A Computable Model of Hereditarily Finite Sets.
Relations, Functions, and Function Sets.
Simple and Primitive Recursion, and the Peano Axioms.
Case Study: The Peano Language.
Binary Relations on a Set.
Case Study: Fixpoint Semantics of Recursive Functions and Lispy.
Sets Come in Different Sizes.
I-Indexed Sets.
From I-Indexed Sets to Sets, and the Axiom of Choice.
Well-Founded Relations, and Well-Founded Induction and Recursion.
Cardinal Numbers and Cardinal Arithmetic.
Classes, Intensional Relations and Functions, and Replacement.
Case Study: Dependent and Polymorphic Types in Maude.
Well Orders, Ordinals, Cardinals, and Transfinite Constructions.
Well-Founded Sets and The Axiom of Foundation.