Abstrakt
The search for pseudorecursive equational theories arose during my translation
of A. I. Maltsev's work in "The Metamathematics of Algebraic Systems."
When
Alfred Tarski heard about the question of a nonrecursive equational
theory
with each n-variable fragment recursive, he felt that this was an interesting
problem, calling such theories pseudorecursive. The first motivation
he
shared centered on showing mathematicians that logic was useful for
making
better mathematics. Later, a surprising second reason became
paramount:
in Tarski's view, the theory constructed was indeed decidable.
This talk
will outline the construction, both motivations, and a program to make
sense
of the second, a claim that a nonrecursive theory may be decidable.