logic-exo7/logic-book.tex at main · exo7math/logic-exo7 · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
\documentclass[11pt]{report}
%\documentclass[10pt,twoside,openright]{report}

\usepackage[screen]{logic}
%\usepackage[print]{logic}


\begin{document}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Title + preface + table of contents
\renewcommand{\contentsname}{Contents}

% Preface
\pagenumbering{roman}
\import{bookmatter/}{preface.tex}
\debutchapitres
\pagenumbering{arabic}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\clearemptydoublepage


%======================================
% Part 1 - True/False Logic
%======================================

\part{True/False Logic}

% 1 - True/False Logic
\import{truefalse/}{truefalse.tex}

% 2 - Proofs
\import{truefalseproofs/}{truefalseproofs.tex}

% 3 - Connectives
\import{connectives/}{connectives.tex}

% 4 - Compactness Theorem
\import{compactness/}{compactness.tex}


%======================================
% Part 2 - First-Order Logic
%======================================

\part{First-Order Logic}

% 5 - First-Order Logic
\import{firstorder/}{firstorder.tex}

% 6 - Variables and Structures
\import{variables/}{variables.tex}

% 7 - Satisfaction
\import{satisfaction/}{satisfaction.tex}

% 8 - Proofs
\import{firstorderproofs/}{firstorderproofs.tex}

% 9 - Soundness Theorem
\import{soundness/}{soundness.tex}

% 10 - Completeness Theorem
\import{completeness/}{completeness.tex}

% 11 - Proof of the Completeness Theorem
\import{completenessproof/}{completenessproof.tex}


%======================================
% Part 3 - Gödel's Incompleteness Theorems
%======================================

\part{Gödel's Incompleteness Theorems}

% 12 - An Overview of Gödel's Incompleteness Theorems
\import{incompletenessoverview/}{incompletenessoverview.tex}

% 13 - Peano Arithmetic
\import{peano/}{peano.tex}

% 14 - Gödel Coding
\import{godelcoding/}{godelcoding.tex}

% 15 - Primitive Recursive Functions
\import{primitiverecursive/}{primitiverecursive.tex}

% 16 - Representable Functions
\import{representablefunctions/}{representablefunctions.tex}

% 17 - Diagonalization
\import{diagonalization/}{diagonalization.tex}

% 18 - Proof of the Incompleteness Theorem
\import{incompletenessproof/}{incompletenessproof.tex}

% 19 - The Second Incompleteness Theorem
\import{secondincompleteness/}{secondincompleteness.tex}


%======================================
% Appendix
%======================================

\import{appendix/}{appendix.tex}

\import{bookmatter/}{postface.tex}
%\newpage

\vfill

\mycenterline{Version 0.3 -- October 2026}

\bigskip
\bigskip

\end{document}