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when he presented his paradox, not necessarily a theory Cantorwho, as mentioned, was aware of several paradoxespresumably had in mind.

Axiomatic theories

Axiomatic set theory was developed in response to these early attempts to understand sets, with the goal of determining precisely what operations were allowed and when.

Consistency

A naive set theory is not necessarily inconsistent, if it correctly specifies the sets allowed to be considered. This can be done by the means of definitions, which are implicit axioms.

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