Theoria: An International Journal for Theory, History and Foundations of Science

Taking into account that no subordering of a scattered partial ordering is dense, we are going to define one idea of rank of a partial ordering which will make possible an equivalent but more operative definition of a scattered partial ordering. Using this notion of rank and the Scott’s sentence associated with the ordering, we are going to characterise in the infinitary language Lw1.w each element of a subclass of the partial orderings, this of the strongly scattered countable partial orderings.

The notion of hyperrandomness is introduced and it is proved that the set of the hyperrandom numbers is effectively inmune but not hyperinmune.