Taken from: Basic technical mathematics : with calculus, metric version, seventh edition by Allyn J. Washington, Logic and computer design fundamentals, second edition, updated by M. Morris Mano and Charles R. Kime. Custom edition for British Columbia Institute of Technology., Book, Published., Peer reviewed
Proceedings of the 18th IEEE Symposium on Logic in Computer Science (LICS-03), Ottawa, ON, 2003. The spectrum of a first-order sentence is the set of cardinalities of its finite models. Relatively little is known about the subclasses of spectra that are obtained by looking only at sentences with a specific signature. In this paper, we study natural subclasses of spectra and their closure properties under simple subdiagonal functions. We show that many natural closure properties turn out to be equivalent to the collapse of potential spectrum hierarchies. We prove all of our results using explicit transformations on first-order structures., Conference paper, Published.