In the early days of the development of model theory it was considered natural and was certainly beneficial to assume that the theories under investigation were in a countable language. The primary advantage of this assumption was the presence of the Omitting Types Theorem of Grzegorczyk, Mostowski, and Ryll-Nardzewski [1], which generalized arguments of Henkin [3] and Orey [8]. Following this,...

This short note mentions several areas of number theory and related parts of mathematics where model theory can potentially offer important new insights. Many of the listed above situations are very well known to number theorists. In some of them one can feel important similarities between two mathematical theories, which are still not formalized and well understood. A model theoretical analysi...

The aim of this chapter is to introduce the reader to the theory of stable groups not to give a rigorous exposition of the general theory. Thus we tend to proceed from the concrete to the abstract, with several examples and analyses of special cases along the way. On the other hand, getting to grips with stable groups presupposes some understanding of the point of view of model theory in genera...

There is an empirical claim that, when exploring a mathematical theory, after a succession of key results have been obtained, a point of equilibrium is reached where any query of interest can be resolved by routine reasoning from the results already established. Here is suggested some ways of thinking about the situation, in general. There are at least some situations where we can establish tha...

We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and completeness results for several natural classes of such logics. Moreover, we show that an entirely general completeness result is not possible. We study the ...

abstractone challenge face political system is implementation national development. there are various models for national development. some countries have relied on import model, but other has emphasis on their indigenous, the purpose of this study is designing intelligence development model in iranian national context. based on the selected theory building methodology, we have theorized intell...

In this paper, we have proposed and analyzed a mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equations.

ground state geometries have been computed using density functional theory (dft) at b3lyp/6-31g(d,p) level of theory. the excitation energies and spectroscopic parameters have been computed using long range corrected (lc) hybrid functional by time dependent density functional theory (tddft) with lc-blyp level of theory. the polarizable continuum model (pcm) has been used for evaluating bulk sol...