Abstract fairness and semantics

AbstractFairness of a program execution, c, is usually expressed such that all objects which are sufficiently often enabled have to occur also sufficiently often in c. There exists a well-known strong equivalence between fair program executions, Π30-formulae, and convergence of initial program executions. However, these results cannot be applied to a study of “fair semantics” of programs, as such a fair semantics is a σ11-formula in general. The main reason therefore is that a semantics does not tell which objects are enabled — only the actually occurring objects are usually seen in semantics. Here we study on a very abstract level some quite natural requirements for semantics s.t. fair semantics with invisible “enabledness” can also be characterized with topological techniques