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  • Qlf2007

    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 \([[1]_0 \mapsto 1]_1\).…

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