axiomatic system
set of axioms from which some or all axioms can be used in conjunction to logically derive theorems
Armstrong's axioms
set of axioms used to infer all the functional dependencies on a relational database
Peano axioms
axiomatic system for the natural numbers
Typographical Number Theory
axiomatic system
Robinson arithmetic
finitely axiomatized fragment of first-order Peano arithmetic that is recursively incompletable (in the sense of Gödel’s incompleteness theorems) and essentially undecidable
Tarski's axioms
first-order axiomatization of a fragment of Euclidean geometry
axiomatic set theory
version of set theory in which axioms are taken as uninterpreted rather than as formalizations of pre-existing truths; defined using a formal logic