For T any completion of Peano Arithmetic and for n any positive integer, there is a model of T of size 2, with no (n + 1)-length sequence of indiscernibles. Hence the Hanf number for omitting typesâ€¦ (More)

Extended Turing Machines We will obtain our simplest model, the ETM, by adding to Turing Machines the ability to add, multiply, and compare real numbers. We allow real parameters to appear in anâ€¦ (More)

It is shown that several natural, undecidable properties of grammars are such that the size of the smallest Turing machine which correctly answers questions of length n grows at a nearly maximal rateâ€¦ (More)