An inductive definition of higher gap simplified morasses (Q2754957)

There is a common feeling that there exists a combinatorial structure the existence of which allows to solve a class of combinatorial problems of set theory. In 1972, in a non-published manuscript, R. B. Jensen introduced the notion of a ``gap-\(\beta\) morass of height \(\kappa\)'' for describing such a structure. Actually, he proved that such morass does exist for any \(\kappa\) regular and \(\beta<\kappa\), assuming \(V=L\).NEWLINENEWLINENEWLINETo investigate the existence of morasses in set theory, several modifications of Jensen's definition have been made, e.g. the notion a simplified morass. \textit{D. Velleman} [J. Symb. Logic 52, 928-938 (1987; Zbl 0639.03051)] has shown that the existence of an \((\omega_0,2)\)-simplified morass is equivalent to the existence of an \((\omega_1,1)\)-simplified morass. That is the starting point of the author's investigations. He presents an inductive definition of higher gap simplified morasses. Moreover, the author studies the relationship of the existence of his morasses to those introduced by R. B. Jensen and Ch. Morgan in his PhD thesis.