In the spring of 1986, I took a course in Model Theory taught by
In that course, Specker lauched a competition for the class: the task was to find a
mathematical description of the smallest 10-dimensional 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 x10+x7+1 which defines the vector space.