Dedekind's "Was sind und was sollen die Zahlen?"

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• Richard Kaye, School of Mathematics, University of Birmingham
• Tuesday 11 October 2016, 16:00-18:00
• Watson Building (Mathematics, R15 on map) Room 310.

If you have a question about this talk, please contact Richard.

Dedekind’s “Was sind und was sollen die Zahlen?” is well known as presenting second order axioms for natural numbers, and proving their categoricity. This is also the work where the notion of “Dedekind finite set” is introduced.

Perhaps less well known is that Dedekind also gives a full proof of the recursion theorem to justify the iteration of functions over the naturals. (Dedekind’s iteration of functions is nearly, but not quite the same as the familiar scheme of primitive recursion. The differences are quite interesting.) Perhaps even more interesting is that Dedekind also gives a “well-ordering theorem” for Dedekind finite sets.

I will lead this discussion, attempting also to put this work into historical context as far as possible. This should be of interest to many people involved in logic, history of maths, philosophy and computer science, and all are welcome.

Richard Kaye, R.W.Kaye@bham.ac.uk http://midlandslogic.org.uk/

Campus map and directions available at http://www.birmingham.ac.uk/visit/maps-and-directions.aspx

This talk is part of the Midlands Logic Seminar series.

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• Midlands Logic Seminar
• Watson Building (Mathematics, R15 on map) Room 310

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