The purpose of these Boolean forms is to specify a particular relation on every linear ordering in a uniform way. We now give a background theorem of independent interest. A set of ordinals is constructible if and only if it is a cross section of some solution to some logical equation whose linear ordering is an ordinal under epsilon. A linear ordering is said to be normal if and only if some initial segment is N under its usual ordering. We then define the ordinal of S as the least ordinal greater than all values of f.
X be a logical equation.
The cardinality of a limit point in a linear ordering is defined to be the cardinality of the set of its predecessors. We now define several classes of linear orderings. Let kappa be an uncountable cardinal. It seems as though Jensen's work on gap n two cardinal theorems should be enough to answer some of these questions. We will report on this later.