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A Cook's Tour of the Finitary Non-Well-Founded Sets | | Samson Abramsky
; | | Date: |
30 Nov 2011 | | Abstract: | We give multiple descriptions of a topological universe of finitary sets,
which can be seen as a natural limit completion of the hereditarily finite
sets. This universe is characterized as a metric completion of the hereditarily
finite sets; as a Stone space arising as the solution of a functorial
fixed-point equation involving the Vietoris construction; as the Stone dual of
the free modal algebra; and as the subspace of maximal elements of a domain
equation involving the Plotkin (or convex) powerdomain. These results
illustrate the methods developed in the author’s ’Domain theory in logical
form’, and related literature, and have been taken up in recent work on
topological coalgebras.
The set-theoretic universe of finitary sets also supports an interesting form
of set theory. It contains non-well founded sets and a universal set; and is
closed under positive versions of the usual axioms of set theory. | | Source: | arXiv, 1111.7148 | | Services: | Forum | Review | PDF | Favorites | |
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