In the spring of 1986, I took a course in Model Theory taught by
Ernst Specker.
In that course, Specker lauched a competition for the class: the task was to find a
mathematical description of the smallest 10dimensional vector space,
using pure logical language, quantors, variables and operation symbols.
The contribution with the least number of letters would win. With the following
description, I had won the book "Model Theory" (Studies in Logic and the Foundations of Mathematics)
by C.C. Chang, H.J. Keisler and most importantly, a signature of Specker (see the last picture below).
All the optimizations to make the formula as compact were indeed necessary:
other contributions from my "commilitones" were close to what I had in size, but no
one was shorter. I had used the algebra system Cayley (now Magma) to find the
irreducible polynomial x^{10}+x^{7}+1 which defines the vector space.
