We consider successor-invariant first-order logic (FO+ succ)inv, consisting of sentences Φ involving an “auxiliary” binary relation S such that (A, S1) |= Φ ⇐⇒ (A, S2) |= Φ for all finite structures A and successor relations S1, S2 on A. A successorinvariant sentence Φ has a well-defined semantics on finite structures A with no given successor relation: one simply evaluates Φ on (A, S) for an a...

The methods used at the Clinical Research Centre, Northwick Park Hospital, to treat wounds potentially infected with neurotropic viruses are outlined. Emphasis is laid on first aid and on surgical attention. Patients should remain under medical supervision for at least four weeks after the injury, the need for specific post-exposure treatment depending on the nature of the exposure.

We prove that for the class of sets of words indexed by countable scattered linear orderings, there is an equivalence between definability in first-order logic, star-free expressions with marked product, and recognizability by finite aperiodic semigroups which satisfy the equation xωx−ω = x. 1998 ACM Subject Classification F.4.1 Mathematical Logic; F.4.3 Formal Languages

Mathematical models described by multivariable functions f(x ) where x 1⁄4 ðx1;...; xnÞ are investigated. If the model output is influenced mainly by low order combinations of input variables x1;...; xn; an attempt can be made to construct a low order approximation to the model using values of f(x ) only. q 2002 Elsevier Science Ltd. All rights reserved.

We propose a model-theoretic framework for investigating profinite structures. We prove that in many cases small profinite structures interpret infinite groups. This corresponds to results of Hrushovski and Peterzil on interpreting groups in locally modular stable and o-minimal structures.

BACKGROUND Anecdotal evidence reported an outbreak of symptoms on Fraser Island during the late 1990 s similar to those expected from exposure to dermotoxins found in the cyanobacterium L. majuscula. This coincided with the presence of a bloom of L. majuscula. METHODS Records from the Fraser Island National Parks First aid station were examined. Information on cyanobacterial blooms at Fraser ...

First Order ID-Logic interprets general first order, nonmonotone, inductive definability by generalizing the wellfounded semantics for logic programs. We show that, for general (thus perhaps infinite) structures, inference in First Order ID-Logic is completeΠ2 over the natural numbers. We also prove a Skolem Theorem for the logic: every consistent formula of First Order ID-Logic has a countable...