The phrase "axiom system" is correct and usable in written English.
It can be used in contexts related to mathematics, logic, or philosophy when discussing a set of axioms that form the basis for a particular theory or framework.
Example: "In order to prove the theorem, we must first establish the axioms of our axiom system."
Alternatives: "axiomatic system" or "system of axioms".
Essay IV: (The Domain of an Axiom System /Axiom System - Operation System. System of Numbers. Arithmetizability of a Manifold. On the Concept of an Operation System.
This axiom system is based on a given set of specificatios for the process synthesis problem.
An axiom system underlying the approach has been constructed to define the combinatorially feasible process structures.
Our first, and main, contribution is to provide an axiom system for XFD implication.
At steady state, we have produced 462 million genotypes per week for each Axiom system.
The Zermelo-Fraenkel axiom system and the special role of the axiom of choice and its various equivalents.
This began his study of axiom systems in projective geometry, which culminated in the highly acclaimed Projective Geometry, 2 vol. (1910 18), in collaboration with John Wesley Young.
Without full-blooded Platonism this cannot be said, because traditional Platonists have no answer to the question "How do mathematicians know which axiom systems describe the mathematical realm?" In contrast, this view entails that all internally consistent axiom systems accurately describe parts of the mathematical realm.
The interest in axiomatic systems at the turn of the century led to axiom systems for the known algebraic structures, that for the theory of fields, for example, being developed by the German mathematician Ernst Steinitz in 1910.
The situation with alternate (and conflicting) axiom systems for set theory is analogous to the 19th-century revolution in geometry that was set off by the discovery of non-Euclidean geometries.
Therefore, full-blooded Platonists can say that when mathematicians lay down axiom systems, all they are doing is stipulating which parts of the mathematical realm they want to talk about.
