Download PDF
Propositional logic
Inference in propositional logic
Axioms for propositional logic
First-order logic
Gödel’s completeness theorem and the compactness theorem
Natural numbers and the successor function
Presberger arithmetic
Orderings
Subtraction and division
Divisors and prime numbers
Modulus and remainders
GCD and LCM
Skolem arithmetic
Löwenheim-Skolem theorem
Robinson arithmetic
First-order peano arithmetic
The fundamental theorem of arithmetic
Finite sequences of natural numbers
Powers, exponents and logarithms of natural numbers
Gödel numbering
The Gödel incompleteness theorems
Second-order logic
Second-order peano arithmetic
Axiom schema of specification and cardinal numbers
Set algebra
The axiom of extensionality
Axiom of adjunction
Algebra of cardinality
Orderings on sets and ordinal numbers
Zermelo–Fraenkel set theory
Axiom of union
The halting problem
Effective procedures
Proof theory
Model theory
The Entscheidungsproblem
Kleene's s-m-n Theorem
Primative recursive functions
Computable functions
General recursive functions
The Ackermann function
The Lambda calculus
Church encoding and Church numerals
Combinatory logic
Functions which can be computed where all loops are of known length in advance. Eg for loops.