axiom→theorem
Axioms are the base; theorems are derived.
Landscape
An overview of the axiom-related conceptual landscape. Domains, relationships, and how terminology connects across logic, mathematics, philosophy, and formal systems.
Domains
Logic & Set Theory
ZFC, first-order logic, axiom of choice. Foundational axiomatic systems.
Mathematics
Euclidean geometry, Peano arithmetic. Axiomatic method in proof and structure.
Philosophy
Self-evident truths, epistemology. Axioms as starting points for reasoning.
Formal Systems
Axiom schemas, inference rules. Syntax and derivation.
Relations
axiom→axiomatic system
Axioms plus inference rules form a system.
axiomatization→axiomaticity
Axiomatization increases axiomaticity of a theory.
axiom-omorphism→domains
Maps connect axiomatic structures across domains.
Overview
The landscape spans from the core term axiom through derivations (axiomatic, axiomatize, axiomatism) and compounds (axiomatic system, axiom of choice) to related concepts (postulate, theorem, lemma). See Glossary and Comparables for details. Glossary · Comparables