[FOM] Duality Theorems and Set Theory +
a_mani_sc_gs at yahoo.co.in
Fri Feb 3 16:04:11 EST 2006
For operators defined on power sets or subsets thereof we know a huge
number of duality results. In some cases the algebraic operations interpreted
on the set may also be required. But it is always (?!) possible to reduce
them to set-theoretic terms. Typically all these are known in ZFC or ZF,
though often we require much less.
Given a set of such operators and some set-theoretic operations, the number of
possible nontrivial derived operators can become finite. This is known in the
topological context, for nonmonotonic operators and other operations and in
other situations. For example, in a topological space (defined Kuratowski
style), the number of non-equivalent operators that we can form with the
closure operator and set theoretic complementation is at most 14 (there is an
associated poset too). For operators on classes too we have too many examples
like in algebra.
My question is about the dependence of the number, the order structure and the
axioms. Any nice papers (recent) on that ?
Member, Cal. Math. Soc
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