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Propositional logic

Inference in propositional logic

Axioms for propositional logic

First-order logic

Gödel's completeness theorem and the compactness theorem

Linguistics

Robinson arithmetic

Peano arithmetic

Orderings

Subtraction and division

Divisors and prime numbers

Modulus and remainders

GCD and LCM

The fundamental theorem of arithmetic

Finite sequences of natural numbers

Powers, exponents and logarithms of natural numbers

Gödel numbering

The Gödel incompleteness theorems

Axiom schema of specification

Set algebra

The axiom of extensionality

Axiom of adjunction

Algebra of cardinality

Second-order logic

Peano axioms

Zermelo–Fraenkel set theory

Axiom of union