Set existence

Hi,

The axiom of comprehension allows us to prove the existence of every
subset of any set having elements in one class (i. e. sharing some
property expressible in the language of first order logic for set
theory). But, what happens with those sets of any given set not
sharing any such property?

I think there is no way in first order logic to express the idea of
'arbitrary combination' of elements of a given set. Wouldn't an aximom
asserting the existence of every such combination be a natural axiom
for set theory?

I would like to find some discussion about this matter in the
literature, or to know why it is not considered important.

Thanks.

.

Relevant Pages

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