[FOM] Duality Theorems and Set Theory +

[A. Mani]

Hello,
         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 ?


Best,

A. Mani
Member, Cal. Math. Soc   
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