[FOM] Mac lane set theory
Thomas Forster
T.Forster at dpmms.cam.ac.uk
Sun Dec 20 11:47:38 EST 2009
There is a body of opinion out there (i suspect not represented on FOM
but...) that holds that Ordinary Mathematics can be captured by Mac lane
set theory (the fragment of Zermelo set theory with Delta-0 separation
instead of full separation).
I take it that the proponents of this view have a reasoned organic view of
ordinary mathematics which is secure enough for them to form a view about
the claims of relevance of replacement, large cardinals etc. They also
have a story about how the view is adequately covered by Mac lane set
theory.
I have never understood this point of view, but i would like to. (These
people who think that Borel Determinacy is not part of ordinary
mathematics - what do they mean and why do they mean it?) In particular i
would like to understand how these people get a non ad-hoc concept out of
what seems - to me - the incredibly ad-hoc (because not time-invariant)
concept of ``ordinary mathematics''. Having grasped that concept i would
then be in the market for arguments that it is all captured by Mac lane
set theory. I suspect the thought is merely that mathematics is to be
identified with the nth order theory of the reals/complexes for n
arbitrarily large, but it might be more interesting than that
If any list-members can point me at any literature where these ideas are
*explained* (as opposed to merely baldy stated) I would be grateful to
them.
Thomas
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