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------------------- 日時：2016年11月14日(月) 16:30--18:00 場所：京都大学 文学部校舎１階 会議室 話者：Prof. Zach Weber (University of Otago) 言語：英語
題目： Paraconsistent set theory and inconsistent mathematics 概要： Paraconsistent set theory takes as axiomatic the `naive' comprehension principle that every collection forms a set. The infamous paradoxes are then just theorems. The background logic that makes this coherently possible is substantially weaker than classical logic; but the expressive power of the theory is substantially stronger than classical set theory. With these competing forces in the background, we will look at two interrelated goals:
Recapture -- reassurance that nothing too important mathematically is lost Expansion -- where new insights and results are gained, studying novel mathematical objects not visible with any other theory
I will survey the development of paraconsistent set theory, showing how the basic properties of ordinal and cardinal numbers can be established, along with new perspectives on `proper classes', the axiom of choice, and the continuum hypothesis. With this foundation, I will mention some further work in inconsistent mathematics: from computability theory, arithmetic, analysis, and topology. Throughout I will call attention to the challenges that this research program faces. -------------------
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