Closure Spaces and Logic by N.m. MartinClosure Spaces and Logic by N.m. Martin

Closure Spaces and Logic

byN.m. Martin, S. Pollard

Paperback | December 7, 2010

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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.
Title:Closure Spaces and LogicFormat:PaperbackDimensions:230 pagesPublished:December 7, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:1441947582

ISBN - 13:9781441947581


Table of Contents

Preface. 1. Logic and Topology. 2. Basic Topological Properties. 3. Some Theorems of Tarski. 4. Continuous Functions. 5. Homeomorphisms. 6. Closed Bases and Closure: Semantics I. 7. Theory of Complete Lattices. 8. Closed Bases and Closure: Semantics II. 9. Truth Functions. Bibliography. Index.