I am a graduate student of philosophy and I'm doing my current
research on an interpretation of Richard Dedekind's works on the
foundations of mathematics as 'axiomatic' and 'structuralistic'.
In the course of this reseach I hit upon some questions that I hope
some of you might be able to answer:
1. Has anybody information about the whereabouts of the letter from
Dedekind to Lachmann mentioned by Emmy Noether in "Gesammelte
mathematische Werke", vol.3, 1932: "So liegt ein Brief des
Zweiundachtigjaehrigen vor - Antwort an einen damaligen Studenten,
Lachmann, jetzt im Besitz von G.Hamel - wo er die 'Erweiterung des
Reichen N der natuerlichen Zahlen zu dem Reiche G der ganzen
rationalen Zahlen' ... andeutet." (p. 490)?
(I've already contacted Prof.Scharlau and the Dedekind-Nachlass in
Goettingen on this matter without success.)
2. Who (and when) was the first to introduce the integers and rational
numbers as equivalence classes of pairs of natural numbers/integers?
3. When was the first proof published, and by whom, that establishes
the isomorphism between any two models for the axioms of the real
numbers?
Any help is kindly appreciated,
from sunny Pittsburgh,
Dirk Schlimm
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Carnegie Mellon University
Department of Philosophy
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address 135 Baker Hall
5000 Forbes Ave.
Pittsburgh, PA 15213
U.S.A.
phone +1 (412) 268-8573
fax +1 (412) 268-1440
e-mail dschlimm@andrew.cmu.edu
http www.contrib.andrew.cmu.edu/user/dschlimm/
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