Prof. Zach Weberレクチャーのお知らせ


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)

Paraconsistent set theory and inconsistent mathematics

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.