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Introduction to Self-Reference and Recursion | |
Introduction to Self-Reference | |
Quotation and Self-Reference | |
Self-Reference in a More General Setting | |
Some Classical Fixed Point Arguments Compared | |
Five fixed Point Arguments | |
A Unification | |
Quasi-Diagonalization | |
How to Silence a Universal Machine | |
Silencing a Universal Machine | |
Some Related Problems | |
Solutions to Problems | |
Some General Incompleteness Theorems | |
Incompleteness | |
Provability by Stages | |
Self-Reference in Arithmetic | |
Normalization and Tarskification | |
Some Special Devices | |
Generalizations | |
Introduction to Formal Systems and Recursion | |
Formal Representability | |
Recursive Enumerability | |
A Universal System and Its Applications | |
A Universal System | |
Enumeration and Iteration Theorems | |
Systems with Effective Properties | |
Arithmetization of Formal Systems | |
Arithmetization of Elementary Formal Systems | |
Double Enumeration | |
More on Arithmetization | |
Elementary Formal Systems and Incompleteness Proofs | |
Truth in Lo Cannot be Formalized | |
A Concrete Incompleteness Proof | |
Double Indexed Relational Systems | |
Indexed Relational Systems | |
Double Indexing | |
Effective Representation Systems | |
Effective Representation | |
Exact and Effective Rosser Systems | |
Fixed Point Theorems in General Setting | |
Sequential Systems | |
Definitions and Purpose | |
Preliminary Definitions | |
Some Fixed Point Properties | |
Summary and Applications | |
Strong Fixed Point Properties | |
The Recursion and Extended Recursion Properties | |
The Myhill Property and Related Properties | |
Summary and Applications | |
Multiple and Fixed Point Properties | |
Double Fixed Points | |
Double Recursion Properties | |
Double Myhill Properties and Related Results | |
Symmetric Functions and Nice Functions | |
Synchronization and Pairing Functions | |
Synchronized Fixed Point Properties | |
Pairing Functions | |
Synchronized Recursion Resumed | |
Some Further Relations Between Fixed Point Properties | |
Single and Double Fixed Point Properties Compared | |
More on Systems of Type 1* | |
Combinators and Sequential Systems | |
Fixed Point Properties of Combinatory Logic | |
Interdefinability of Some Combinators | |
Fixed Points | |
Multiple Fixed Points | |
Formal Combinatory Logic | |
The Axiom Systems CL and CLo. | |
A Second Variety of Fixed Point Theorems | |
Self-Reference in CLo | |
Fixed Point Theorems of the Second Type | |
Extended Sequential Systems | |
Table of Contents provided by Publisher. All Rights Reserved. |
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The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.