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The spectrum of a first-order sentence is the set of cardinalities of its finite models. This paper is concerned with spectra of sentences over languages that contain only unary function symbols. In particular, it is shown that a set S of natural numbers is the spectrum of a sentence over the language of one unary function symbol precisely if S is an… (More)
We show that the set of square numbers is the spectrum of an F 1 1;1-sentence (existential second order logic with quantiication over unary function variables) with two unary function variables, but it is not the spectrum of F 1 1;1-sentences with only one unary function variable.
This article provides a review of the routine methods currently utilized for total naphthenic acid analyses. There is a growing need to develop chemical methods that can selectively distinguish compounds found within industrially derived oil sands process affected waters (OSPW) from those derived from the natural weathering of oil sands deposits. Attention… (More)