This paper attempts to serve as an introduction to abstract model theory. We introduce the notion of abstract logics, explore first-order logic as an instance of and as the basis for abstract logics, and end by proving Lindström’s theorem.

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Axiomatizations of the General Theory of Relativity.have occasionally been conducted to achieve precision and clarification of underlying concepts. Rigorous and inspiring work towards that aim based on first-order logic has been performed by Professor Németi and his working group (see references below). A complementary approach (Benda 2008) constructs the relativistic spacetime manifold ab init...

The kinetics and mechanism of the reaction between benzaldehyde 1, malononitrile 2 and dimedone 3 in a mixture of ethanol and water as solvents in the presence of fructose as a biodegradable catalyst has been studied by the spectroscopic method (UV-Vis spectrophotometry method). The influence of various parameters (temperature, solvent and concentration) was studied on the reaction by means of ...

In this study, nanoporous silica aerogel and silica aerogel-activated carbon composites have been synthesized using a water glass precursor by cost effective ambient pressure drying method. Equilibrium and kinetics of benzene and ethyl benzene adsorption on silica aerogel and its composites have been measured in a batch mode at tree weights of adsorbent. For the first time, the experimental dat...

We consider fragments of first-order logic over finite words. In particular, we deal with first-order logic with a restricted number of variables and with the lower levels of the alternation hierarchy. We use the algebraic approach to show decidability of expressibility within these fragments. As a byproduct, we survey several characterizations of the respective fragments. We give complete proo...

Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic. A few of these results non-trivially generalize known interpolation results; all the others are new. We also discuss some applications of our results to the theory of institutio...

In this paper we consider the partial many-sorted first-order logic and its extension to the subsorted partial many-sorted first-order logic that underly the Casl specification formalism. First we present counterexamples showing that the generalization of the Craig Interpolation Property does not hold for these logics in general (i.e., with respect to arbitrary signature morphisms). Then we for...