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# Qlf2007

My favorite wikis
• ## The Position Theory

July 19, 2015 by Qlf2007

The position theory serves as a radical extension to the Veblen function. The Veblen function allows transfinitely many variables arranged on a row, each having an ordinal as its position, e.g. $$\phi(1[\omega])$$

The position theory adds more positions to Veblen function. The traditional positions are now $$0$$-positions. A $$1$$-position is a function from $$0$$-positions to ordinals, s.t. only finite positions are mapped to non-zero ordinals. They are ordered like decimal numbers. If positions $$p,q$$ both map all positions $$[\alpha']_0 > [\alpha]_0$$ to equal ordinals and $$p([\alpha]_0) > q([\alpha]_0)$$ then $$p$$ is stronger than $$q$$. The first $$1$$-position that does not degenerate to a $$0$$-position is $$[[1]_0 \mapsto 1]_1$$.…