Activity: Talk or presentation › Invited talk › Popular
Description
A theory is restricted if there is a fixed bound on the complexity of its axioms.
Kenneth McAloon proves that every restricted arithmetical theory that is consistent with Peano Arithmetic has a model in which the standard natural numbers are definable.
In this talk we discuss the idea of generalizing McAloon's result to the class
of consistent restricted sequential theories. We only obtain a weaker statement for the more general case. Whether the stronger statement holds remains open.
In the talk, we briefly indicate how McAloon's proof works and discuss some immediate generalizations. Then, we will outline the basic ideas behind the proof of the result concerning consistent restricted sequential theories.