Re: -- Lucky with Erdos-Woods numbers?

In article <47C8AC55.8040301@xxxxxx>,
Rainer Rosenthal <r.rosenthal@xxxxxx> wrote:

Rainer Rosenthal wrote:

http://www.research.att.com/~njas/sequences/A059756 comment:
Alan R. Woods, Thesis, 1981
[I would like more information about this reference! - njas]

The order of years (Thesis 1981, Book 1984) suggests a deeper
connection. It's great fun to explore the information jungle :-)

There is a paper online available
http://www.mathp6.jussieu.fr/~miw/articles/pdf/odp.pdf

Open Diophantine Problems
Michel Waldschmidt
Moscow Mathematical Journal
Vol. 4, No. 1, Jan-Mar 2004, pp. 245-305

This paper gives important information with respect to A059756
and Neil Sloane's second question. See for example page 255
with Conjecture 2.2 (Erdös-Woods). The comment says:

Conjecture 2.2 is motivated by the following
question raised by J. Robinson:
Is first order arithmetic definable using only
the successor function S: x |--> x+1
and the coprimarity x _|_ y <==> (x,y) = 1?
It would suffice to decide whether the function
x |--> x^5 can be defined in the language (S,|_);
see [Woo], [Guy, B29 and B35], [BLSW]

And there we are:

[Woo] A. Woods, Some problems in logic and number theory,
Ph.D. thesis, Manchester, 1981

There is an Alan Woods at U Western Australia,
http://www.maths.uwa.edu.au/~woods/
don't know whether he's your man.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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