Theory Exploration: a role for Model Theory?

Abstract

There is an empirical claim that, when exploring a mathematical theory, after a succession of key results have been obtained, a point of equilibrium is reached where any query of interest can be resolved by routine reasoning from the results already established. Here is suggested some ways of thinking about the situation, in general. There are at least some situations where we can establish that all results (of a certain shape) will follow by routine reasoning from a small number of key properties. An example is described, and the significance for automated theory exploration discussed.