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

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• Richard Kaye, School of Mathematics, University of Birmingham
• Tuesday 18 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.

A continuation of our discussion of Dedekind’s “Was sind und was sollen die Zahlen?”

In this paper, Dedekind in fact claims to show that every Dedekind finite set is equinumerous to a bounded subset of the natural numbers. We now know that this theorem requires some form of the axiom of choice. It is interesting to read Dedekind’s proof and identify where this appeal to Choice is made, and whether or not it is a “mistake”. It is also interesting to speculate on how close Dedekind actually got to Zermelo’s proof of the Well ordering principle, something that would not appear until over 40 years later.

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.

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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