A System for Models of First Order Theories

If you want to know whether a property is true or not in a specific algebraic structure,you need to test that property on the given structure. This can be done by hand, which can be cumbersome and erroneous. In addition, the time consumed in testing depends on the size of the structure where the property is applied. We present an implementation of a system for finding counterexamples and testing properties of models of first-order theories. This system is supposed to provide a convenient and paperless environment for researchers and students investigating or studying such models and algebraic structures in particular. To implement a first-order theory in the system, a suitable first-order language.( and some axioms are required. The components of a language are given by a collection of variables, a set of predicate symbols, and a set of operation symbols. Variables and operation symbols are used to build terms. Terms, predicate symbols, and the usual logical connectives are used to build formulas. A first-order theory now consists of a language together with a set of closed formulas, i.e. formulas without free occurrences of variables. The set of formulas is also called the axioms of the theory. The system uses several different formats to allow the user to specify languages, to define axioms and theories and to create models. Besides the obvious operations and tests on these structures, we have introduced the notion of a functor between classes of models in order to generate more co~plex models from given ones automatically. As an example, we will use the system to create several lattices structures starting from a model of the theory of pre-orders.

Towards a better understanding of the relationship between speed of internationalization and performance outcomes among young international ventures

This thesis offers an explanation for the inconsistent relationship between speed of internationalization and performance outcomes in the context of young international ventures. We argue that the variables of scope of internationalization, entrepreneurial orientation and degree of internationalization play a moderating role in the relationship between speed of internationalization and performance outcomes of international new ventures (INVs). Using primary survey data from INVs in China, we found empirical support for significant moderating impact of scope of internationalization, entrepreneurial orientation variables and no support for the moderating impact of degree of internationalization variable. The results suggest that business managers of INVs shall consider the applied moderating variables as an effective tool kit to enhance firm performance in foreign markets and to mitigate any potential risks of early internationalization.