elementary differences among jump hierarchies

Fudan Univ, Software Sch, Univ Leeds, Univ WisconsinIt is shown that Th(H-1) not equal Th(H-n) holds for every n > 1, where H_ is the upper semi-lattice of all high(m) computably enumerable (c.e.) degrees for m > 0, giving a first elementary difference among the highness hierarchies of the c.e