  We formulate a general abstract criterion for verifying the local-to-global
principle for a rigidly-compactly generated tensor triangulated category. Our
approach is based upon an inductive construction using dimension functions.
Using our criterion we give a new proof of the theorem that the local-to-global
principle holds for such categories when they have a model and the spectrum of
the compacts is noetherian. As further applications we give a new set of
conditions on the spectrum of the compacts that guarantee the local-to-global
principle holds and use this to classify localising subcategories in the
derived category of a semi-artinian absolutely flat ring.
