1 Propositional Logic
1.1  Syntax
1.2  The propositional calculus
1.3  Semantics
1.4  Soundness and completeness
2 First-Order Predicate Logic
2.1  Syntax
2.2  The first-order predicate calculus
2.3  Semantics
2.4  Functions and identity
2.5  Soundness
3 Completeness
3.1  Cardinalities
3.2  Planning the completeness proof
3.3  The completeness proof
3.4  Unintended models
4 Theories
4.1  Arithmetic
4.2  Set theory
4.3  Sets and numbers
4.4  Unintended models, again
5 Computability
5.1  The Entscheidungsproblem
5.2  Computable functions
5.3  Uncomputable functions
5.4  Decidability
5.5  Coding
6 Turing Computability
6.1  Turing machines
6.2  Computing arithmetical functions
6.3  Universal Turing machines
6.4  Uncomputability
7 Recursive Functions
7.1  Primitive recursive functions
7.2  Primitive recursive operations
7.3  Unbounded search
7.4  Recursiveness and Turing-computability
7.5  Feasible computation
8 Arithmetization
8.1  Expressing functions and relations
8.2  Representability
8.3  Conditions for representability I
8.4  Conditions for representability II
8.5  Wrapping up
9 Incompleteness
9.1  Preview
9.2  Arithmetization of syntax
9.3  The First Incompleteness Theorem
9.4  Tarski’s Theorem
9.5  The arithmetical hierarchy
10 The Unprovability of Consistency
10.1  The Second Incompleteness Theorem
10.2  Löb’s Theorem
10.3  The logic of provability
10.4  Chaitin’s Incompleteness Theorem
10.5  Philosophy of mind