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Closure Spaces and Logic (Paperback, Softcover reprint of hardcover 1st ed. 1996)
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Closure Spaces and Logic (Paperback, Softcover reprint of hardcover 1st ed. 1996)
Series: Mathematics and Its Applications, 369
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This book examines an abstract mathematical theory, placing special
emphasis on results applicable to formal logic. If a theory is
especially abstract, it may find a natural home within several of
the more familiar branches of mathematics. This is the case with
the theory of closure spaces. It might be considered part of
topology, lattice theory, universal algebra or, no doubt, one of
several other branches of mathematics as well. In our development
we have treated it, conceptually and methodologically, as part of
topology, partly because we first thought ofthe basic structure
involved (closure space), as a generalization of Frechet's concept
V-space. V-spaces have been used in some developments of general
topology as a generalization of topological space. Indeed, when in
the early '50s, one of us started thinking about closure spaces, we
thought ofit as the generalization of Frechet V space which comes
from not requiring the null set to be CLOSURE SPACES ANDLOGIC XlI
closed(as it is in V-spaces). This generalization has an extreme
advantage in connection with application to logic, since the most
important closure notion in logic, deductive closure, in most cases
does not generate a V-space, since the closure of the null set
typically consists of the "logical truths" of the logic being
examined."
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