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- verb Alternative spelling of
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Most scientific theories contain analytic (i.e., a priori) and synthetic elements, and it is necessary to axiomatise them in order to distinguish the two clearly.
ZF arose as an attempt to axiomatise the theory of wellfounded sets, and this principle is kept constantly in mind by the ZF-istes as they struggle to find new and more informative axioms.
There is no doubt that restricting attention to wellfounded sets (in the sense that it is them alone that one tries to axiomatise) concentrated the minds of 20th century mathematicians to great effect.