User blog comment:Qlf2007/The Position Theory/@comment-99.185.0.100-20150805165556

Actually, I believe the first non-degenerate w-position in BEAF is X{X}X. We need an extension to the positions (i.e. mapping $$\alpha$$ onto $$\alpha$$-positions for any ordinal $$\alpha$$) to continue the position theory up to XX, the next position type to get XX, and arbitrary TYPES only get up to {X,X,1,1,2}. Having a type-$$\alpha$$ $$\beta$$-position be a <$$\alpha$$,$$\beta$$>-position and extending it like the Veblen hierarchy only gets to {X,X(1)2}!!