以下の要領でCAPEレクチャーが開催されます。皆様のご参加をお待ちしております。
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
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.