Nonlinearity, Complexity and Foundations in Mathematics

On the limits of comparing subset sizes within ℕ

speaker: Sylvia Wenmackers (Katholieke Universiteit Leuven )

abstract: This talk reviews different ways of assigning ‘sizes’ to subsets of the natural numbers: Cantor’s cardinality theory and Norton’s infinite lottery logic with mirror cardinalities, natural and generalised density from number theory, Benci’s numerosity theory, and a recent reconstruction of Bolzano’s work by Trlifajová. We can relate these formalisms to each other in terms of the underlying limit operations. By comparing them in terms of constructiveness, uniqueness, and totality, we get a better grip on the intrinsic limitations in determining the sizes of subsets of ℕ.

timetable:
Fri 13 Sep, 10:20 - 10:55, Aula Dini
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