axjomatyk
Axjomatyk is the study of axiomatic systems and their foundations across mathematics, logic, and related disciplines. It examines how axioms are chosen, organized into systems, and used to derive theorems within formal languages. The field emphasizes metatheory, including questions of consistency, independence, completeness, and decidability; the relationships between axioms, rules of inference, and models; and the methods by which different axiom systems can be compared or translated into one another.
Core methods in axjomatyk include proof theory, model theory, and, in some approaches, category-theoretic or type-theoretic
Historically, axiomatics emerged from foundational efforts in geometry and arithmetic and developed into a general methodology
In terms of applications, axjomatyk informs formal verification of software and hardware, specification and reasoning about