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An Introduction to Gödel's Theorems
Bibliography
monograph
Author(s):
Peter Smith
Publication date
(Online):
2009
Publisher:
Cambridge University Press
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Book Chapter
Pages
: 372-382
DOI:
10.1017/CBO9781139149105.049
SO-VID:
0b4c3277-3730-4302-9fd1-839c8f25c9a9
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Book chapters
pp. xiii
Preface
pp. 1
What Gödel's Theorems say
pp. 8
Functions and enumerations
pp. 14
Effective computability
pp. 25
Effectively axiomatized theories
pp. 36
Capturing numerical properties
pp. 46
The truths of arithmetic
pp. 49
Sufficiently strong arithmetics
pp. 53
Interlude: Taking stock
pp. 56
Induction
pp. 62
Two formalized arithmetics
pp. 71
What Q can prove
pp. 83
IΔ0, an arithmetic with induction
pp. 90
First-order Peano Arithmetic
pp. 97
Primitive recursive functions
pp. 113
LA can express every p.r. function
pp. 119
Capturing functions
pp. 124
Q is p.r. adequate
pp. 130
Interlude: A very little about Principia
pp. 136
The arithmetization of syntax
pp. 144
Arithmetization in more detail
pp. 152
PA is incomplete
pp. 161
Gödel's First Theorem
pp. 167
Interlude: About the First Theorem
pp. 177
The Diagonalization Lemma
pp. 185
Rosser's proof
pp. 191
Broadening the scope
pp. 197
Tarski's Theorem
pp. 201
Speed-up
pp. 204
Second-order arithmetics
pp. 219
Interlude: Incompleteness and Isaacson's Thesis
pp. 233
Gödel's Second Theorem for PA
pp. 239
On the ‘unprovability of consistency’
pp. 245
Generalizing the Second Theorem
pp. 252
Löb's Theorem and other matters
pp. 258
Deriving the derivability conditions
pp. 262
‘The best and most general version’
pp. 272
Interlude: The Second Theorem, Hilbert, minds and machines
pp. 285
μ-Recursive functions
pp. 297
Q is recursively adequate
pp. 300
Undecidability and incompleteness
pp. 310
Turing machines
pp. 321
Turing machines and recursiveness
pp. 328
Halting and incompleteness
pp. 338
The Church–Turing Thesis
pp. 348
Proving the Thesis?
pp. 367
Looking back
pp. 370
Further reading
pp. 372
Bibliography
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