Titlebook: Closure Spaces and Logic; Norman M. Martin,Stephen Pollard Book 1996 Springer Science+Business Media Dordrecht 1996 Division.Homeomorphism

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y 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 ou

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https://doi.org/10.1007/978-3-540-75259-2attices are rich in diverse and interesting models from apparently far-flung fiields. They were . to stimulate an abundance of interpretations, any constriction of vision to a privileged model being shunned on principle. (Set theoretic axioms may be an exception, but we question whether they . to be. See Pollard, ch. 9.)

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A. Die Abstammung des Versuchsmaterials,lso, the desirable properties of correct valuations uncovered in ch. 4.) To a great extent, however, maximally consistent sets behave like models because they have topological properties more abstract than maximal consistency itself. We shall explore one of these more abstract properties — namely, membership in a closed basis.

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Theory of Complete Lattices,er and Cl(UW) is the least upper bound of each subset W of C. It is convenient to let ‘. W’ and ‘(A.B)’ designate Cl(∪ W) and Cl(A∪B), respectively. (. is the operation of ..) In this chapter, we use wellknown properties of lattices to derive some theorems about closure spaces.

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Closed Bases and Closure Semantics I,ound and complete logic induces a natural pairing between these sets and elementary equivalence classes of the more usual model structures. (Recall, also, the desirable properties of correct valuations uncovered in ch. 4.) To a great extent, however, maximally consistent sets behave like models beca