A New Proof of the Mckinsey-tarski Theorem
نویسنده
چکیده
It is a landmark theorem of McKinsey and Tarski that if we interpret modal diamond as closure (and hence modal box as interior), then S4 is the logic of any dense-initself metrizable space [14, 17]. The McKinsey-Tarski Theorem relies heavily on a metric that gives rise to the topology. We give a new and more topological proof of the theorem, utilizing Bing’s Metrization Theorem [8, 10].
منابع مشابه
A new proof for the Banach-Zarecki theorem: A light on integrability and continuity
To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...
متن کاملAnother proof of Banaschewski's surjection theorem
We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...
متن کاملQuantified Modal Logic on the Rational Line
In the topological semantics for propositional modal logic, S4 is known to be complete for the class of all topological spaces, for the rational line, for Cantor space, and for the real line. In the topological semantics for quantified modal logic, QS4 is known to be complete for the class of all topological spaces, and for the family of subspaces of the irrational line. The main result of the ...
متن کاملThe Basic Theorem and its Consequences
Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...
متن کاملA New Proof of Completeness of S4 with Respect to the Real Line
It was proved in McKinsey and Tarski [7] that every finite wellconnected closure algebra is embedded into the closure algebra of the power set of the real line R. Pucket [10] extended this result to all finite connected closure algebras by showing that there exists an open map fromR to any finite connected topological space. We simplify his proof considerably by using the correspondence between...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017