In this paper we study the theory Q. We prove a basic result that says that, in a sense explained in the paper, Q can be split into two parts. We prove some consequences of this result. (i) Q is not a poly-pair theory. This means that, in a strong sense, pairing cannot be defined in Q. (ii) Q does not have the Pudlák Property. This means that there two interpretations of S21 in Q which do not have a definably isomorphic cut. (iii) Q is not sententially equivalent with PA-. This tells us that we cannot do much better than mutual faithful interpretability as a measure of sameness of Q and PA-. We briefly consider the idea of characterizing Q as the minimal-in-some-sense theory of some kind modulo some equivalence relation. We show that at least one possible road towards this aim is closed.
CITATION STYLE
Visser, A. (2017). On Q. Soft Computing, 21(1), 39–56. https://doi.org/10.1007/s00500-016-2341-5
Mendeley helps you to discover research relevant for your work.