A new set of postulates for betweenness, with proof of complete independence

in which the number of postulates is reduced to five. Moreover, the new postulate 9 itself is easier to remember and more convenient to handle than any of the other postulates 1-8. The addition of this new postulate makes desirable an extension of the discussion of the earlier paper so as to include all thirteen of the basic postulates; and this extension has been made in the present paper. Finally, the postulates of the new set (12) are shown to be completely independent in the sense of E. H. Moore. (In regard to the other sets, a