| There is as yet no warrant for ruling out an arithmetical set that is not decidable, or for ruling out a decidable set that is not arithmetical. |
| Which mathematical theory best describes real space is an empirical issue, not decidable independently of physical considerations. |
| There are uncountably many subsets of N, but since there are only countably many Turing machines, there can be only countably many decidable sets. |
| Moreover, the geometries axiomatized in the book have consistent and decidable extensions, namely, Euclidean or hyperbolic geometry over real-closed fields. |
| The novelty of OWL-E is that it enhances OWL DL with much more datatype expressiveness and it is still decidable. |
| We prove here that the finite power property is decidable for rational sets of the free group. |
