Limiting Cases for Spectrum Closure Results

  • Aaron Hunter Simon Fraser University, Burnaby

Abstract

The spectrum of a first-order sentence is the set of cardinalities of its finite models. Given a spectrum S and a function f, it is not always clear whether or not the image of S under f is also a spectrum. In this paper, we consider questions of this form for functions that increase very quickly and for functions that increase very slowly. Roughly speaking, we prove that the class of all spectra is closed under functions that increase arbitrarily quickly, but it is not closed under some natural slowly increasing functions.

Author Biography

Aaron Hunter, Simon Fraser University, Burnaby
Published
2004-10-26
How to Cite
HUNTER, Aaron. Limiting Cases for Spectrum Closure Results. The Australasian Journal of Logic, [S.l.], v. 2, oct. 2004. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/1768>. Date accessed: 15 nov. 2019. doi: https://doi.org/10.26686/ajl.v2i0.1768.