“Decorated Linear Order Types and the Theory of Concatenation,” with Vedran Čačić, Pavel Pudlák, Alasdair Urquhart and Albert Visser, p. 1–13 in Logic Colloquium 2007, ed. F. Delon, U. Kohlenbach, P. Maddy and F. Stephan, Cambridge University Press, 2010.
We study the interpretation of Grzegorczyk’s Theory of Concatenation TC in structures of decorated linear order types satisfying Grzegorczyk’s axioms. We show that TC is incomplete for this interpretation. What is more, the first order theory validated by this interpretation interprets arithmetical truth. We also show that every extension of TC has a model that is not isomorphic to a structure of decorated order types.
We provide a positive result, to wit, a construction that builds structures of decorated order types from models of a suitable concatenation theory. This construction has the property that if there is a representation of a certain kind, then the construction provides a representation of that kind.
You are welcome to download and read this document. I welcome feedback on it. Please check the final published version if you wish to cite it. Thanks.
I’m Greg Restall, and this is my personal website. ¶ I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the Director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology ¶ I like thinking about – and helping other people think about – logic and philosophy and the many different ways they can inform each other.