​Univalent Foundations and the Equivalence Principle by Benedikt Ahrens (INRIA Nantes, France)

Talk at: FOMUS 2016. For all Talks and more information, slides etc. see: http://fomus.weebly.com/ ​Univalent Foundations and the Equivalence Principle by Benedikt Ahrens (INRIA Nantes, France) Abstract: ​The "equivalence principle" (EP) says that meaningful statements in mathematics should be invariant under the appropriate notion of equivalence - "sameness" - of the objects under consideration. In set theoretic foundations, the EP is not enforced; e.g., the statement "1 ϵ Nat" is not invariant under isomorphism of sets. In univalent foundations, on the other hand, the equivalence principle has been proved for many mathematical structures. In this introductory talk, I first give an overview of earlier attempts at designing foundations that satisfy some invariance property. Afterwards I present results, both by other and myself, on the validity of EP in univalent foundations. This workshop was organised with the generous support of the Association for Symbolic Logic (ASL), the Association of German Mathematicians (DMV), the Berlin Mathematical School (BMS), the Center of Interdisciplinary Research (ZiF), the Deutsche Vereinigung für Mathematische Logik und für Grundlagenforschung der Exakten Wissenschaften (DVMLG), the German Academic Merit Foundation (Stipendiaten machen Programm), the Fachbereich Grundlagen der Informatik of the German Informatics Society (GI) and the German Society for Analytic Philosophy (GAP).