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G. Sambin, A new and elementary
method to represent every complete boolean algebra
It is shown, in a completely constructive way, that every cBa is isomorphic
to the phase space over a semilattice with a downward closed subset
as dualizer.
T. Coquand - S. Sadocco - G. Sambin - J. Smith,
Formal topologies on the set of first order formulae
Two covers on the set of formulae, both of which can be used for a proof
of completeness of the semantics of formal topologies, are shown to
be distinct. This allows to realize in a precise way that Henkin sets,
that is models, are just the same as formal points on one of the two
covers.
G. Battilotti - G. Sambin,
Pretopologies and a uniform presentation of sup-lattices, quantales
and frames
Some well known results about presentations are obtained in a uniform
and simple way by means of pretopologies. The paper also analyses which
definitions and which proofs can be obtained predicatively. Moreover,
the correspondence with Johnstone's notion of coverage is analysed in
detail.
G. Sambin, Some points in formal
topology
This is a survey (dated end of 2001) of my approach to constructive
topology. Part 1 contains the first definition of formal topology (given
in [Sambin87]) and a summary of its developments, with references. Part
2 is a short but complete introduction to the new approach which I call
the basic picture, with main definitions. Part 3 contains a survey of
the views I have developed on the philosophical meaning of constructivism
in mathematics, topology in particular.
The story continues with papers on the Basic Picture.