EXAMPLES IN DEPENDENT THEORIES

Examples in dependent Theories

In the first part we show a counterexample to a conjecture by Shelah regarding the existence of indiscernible sequences in dependent theories (up to the first inaccessible cardinal). In the second part we discuss generic pairs, and give an example where the pair is not dependent. Then we define the notion of directionality which deals with counting the number of coheirs of a type and we give ex...

Central and Local Limit Theories in Markov Dependent Random Variables

Examples of admissible simplification of mathematical theories

cation of mathematical models, questionnaire " Mathematicians, like physicists, are pushed by a strong fascination. Research in mathematics is hard, it is intellectually painful even if it is rewarding , and you wouldnt do it without some strong urge. " [D. Ruelle]. We shall give some examples from our experience, when we were able to simplify some serious mathematical models to make them under...

Basic examples on physical gauge theories

Let us start with a very illustrative and simple example. It is taken from [1] (in an abbreviated form) and, as far as we know, it is not a historical example, but looking into retrospective it has some connections with the ideas introduced in 1926 by V. Fock [7] shortly after E. Schrödinger stated his equation. We are going to use the kind of first quantization arguments that a pioneer of quan...

Maverick Examples Of Coset Conformal Field Theories

We present coset conformal field theories whose spectrum is not determined by the identification current method. In these “maverick” cosets there is a larger symmetry identifying primary fields than under the identification current. We find an A-D-E classification of these mavericks.