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| ``Sudan''
by para0doxa on 2004-05-03 12:33:13 |
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Read this:
http://mathforum.org/epigone/math-history-list/smixsmeeblu
Subject: Ackermann vs. Sudan function: priority of discovery [was:Ackermann - or Budan or ?]
Author: Bill Dubuque <wgd@martigny.ai.mit.edu>
Organization: MIT
Date: Fri, 12 Sep 1997 08:09:48 -0400
The following message is a courtesy copy of an article
that has been posted as well.
mac@abacus.concordia.ca ( JOHN MCKAY ) writes:
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| Can someone assess who originated the so-called "Ackermann fn" ?
| It appears it may not be Ackermann.
Cristian Calude has written a number of papers on the history
of the Ackermann and Sudan functions, e.g. see
Calude, Cristian; Marcus, Solomon; \cedla Tevy, Ionel
The first example of a recursive function which is not primitive recursive.
Historia Math. 6 (1979), no. 4, 380--384. MR 80i:03053 03D20 01A60
Chronologically, Sudan's function is the first example of a recursive
but not primitive recursive function (Bull. Math. Soc. Roumaine Sci.
30 (1927), 11 - 30; Jbuch 53, 171). Ackermann's work was published
slightly later (Math. Ann. 99 (1928), 118 - 133; Jbuch 54, 56). Both
were students of Hilbert, and were working on a problem posed by
Hilbert, and were acquainted with each other's work. Sudan's function
extends to ordinals and majorizes Ackermann's function (except at
a single point). As Smorynski says in his book Logical Number Theory
independently, to two of Hilbert's students, Wilhelm Ackermann and
Gabriel Sudan. Although they gave essentially the same recursion,
Sudan worked with functions of transfinite ordinals and Ackermann
with functions of natural numbers, whence Hilbert cited Ackermann
and Ackermann's is the name associated with the resulting functions.
The paper cited above also has speculations as to why Hilbert and
Bernays did not mention Sudan's construction.
According to MR 82k:03061, Sudan's function is as follows
F (x, y) = x+y
0
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