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

✍ Scribed by José Meseguer.

Tongue
English
Leaves
183
Category
Library
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✦ Synopsis

University of Illinois at Urbana-Champaign Urbana, IL 61801, USA, 2011. β€” 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.

✦ Subjects

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