The partial ordering of Medvedev reducibility restricted to the family of 1 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a 1 class, which we call a “c.e. separating class”. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by...

Church-Turing Thesis: Claim that every computable function can be computed by a Turing machine. Computability theory: Study of computable functions on the natural numbers. Continuum hypothesis: Conjecture that there are only two sizes of infinite sets of real numbers. Database: Finite, typically relational structure. First order logic: Mathematical model of the part of language built up from th...

introduction determining the importance of environmental impacts is one of the main issues and concerns in the process of environmental impact assessment (eia) of projects. ecological impacts assessment is very complicated and requires estimates and anticipates of all environmental impacts and thus always associated with uncertainty. a major problem in assessment of ecological impacts is that t...

We study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. We discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. This first part introduces the main conceps and philosophies anddiscu...

We study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. We discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. This second part continues to study the question of catecoricitytrans...

First-order predicate logic meets many problems when used to explain or reproduce cognition and intelligence. These problems have a common nature, that is, they all exist outside mathematics, the domain for which mathematical logic was designed. Cognitive logic and mathematical logic are fundamentally different, and the former cannot be obtained by partially revising or extending the latter. A ...

this paper examines critically the contributions of cournot, jevons and walras as the founders of classical mathematical economics from a methodological standpoint. advances in different economic schools and doctrines in the 19th century produced an environment of multi-dimensionality in economic analysis which was regarded by the pioneers of classical mathematical economists as a chaotic state...