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.

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...

Semantic attachment is provided by FOL as a means for associating model values (i.e. LISP code) to symbols of a first order language. This paper presents an algorithm that automatically generates semantic attachments in FOL and discusses the advantages deriving from its use.

Ordinary first-order logic has the property that two formulas φ and ψ have the same meaning in a structure if and only if the formula φ ↔ ψ is true in the structure. We prove that independence-friendly logic does not have this property. §

A method for encoding formulas in rst-order logic with equality into some equational logics and their associated propositional logics is presented. This yields some new strategies for theorem-proving in rst-order logic with equality. We outline the techniques and give a simple illustration of their use.

Solving equations is one of the main themes in mathematics. A large part of the combinatorial group theory revolves around the word and conjugacy problems particular types of equations in groups. Whether a given equation has a solution in a given group is, as a rule, a non-trivial problem. A more general and more difficult problem is to decide which formulas of the first-order logic hold in a g...

We consider the restriction of first–order logic to models, called pseudo– finite, with the property that every first–order sentence true in the model is true in a finite model. We argue that this is a good framework for studying first-order logic on finite structures. We prove a Lindström Theorem for extensions of first order logic on pseudo-finite structures.