ABSTRACT
Chapter examines random sets as a basis to carry structures modeling towards a competitive culmination problem where models “compete” based on modeling game trees. A model rank is higher when on game trees with a higher game tree degree, satisfies goals, hence realizing specific models where the plan goals are satisfied. Characterizing competitive model degrees on random sets is a basic area to explore. A model is a competing model iff at each stage the model is compatible with the goal tree satisfiability criteria. Compatibility is defined on Random Sets where the correspondence between compatibility on random sets and game tree degrees are applied to present random model diagrams. Random diagram game degrees are applied and model ranks based on satisfiability computability to optimal ranks are examined.
