Independence results in mathematics are relative to a given axiomatic system. For example, the logical independence of the parallel postulate was established, relative to the other axioms of Euclidean geometry, during the nineteenth century.
The independence results most of interest in contemporary mathematics are for the most part relative to the axioms of ZFC set theory, the de facto standard foundational system. Other independence results concern Peano arithmetic and other formalizations of the natural numbers.
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