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Axiomatization is a category for books that build, analyze, or critique entire fields by stating primitive concepts and explicit axioms, then deriving results with rigorous logic. These works prioritize structural clarity and minimal assumptions, often addressing issues like consistency, completeness, independence, equivalence of axiom systems, and decidability. The category spans foundational mathematics and logic (e.g., set theory, arithmetic, geometry), axiomatic treatments in sciences and social sciences (thermodynamics, quantum theory, probability, utility and game theory), and meta-level studies such as proof theory, model theory, and formal verification. Many titles also explore the history and philosophy of the axiomatic method, including its power and limits. Typical features include precise definitions, axiom lists, theorems with proofs, metatheorems, and comparisons of alternative frameworks, all aimed at turning intuition into a transparent, traceable structure.

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