FRIEDMAN-WEIERMANN STYLE INDEPENDENCE RESULTS BEYOND PEANO ARITHMETIC

Title & Authors
FRIEDMAN-WEIERMANN STYLE INDEPENDENCE RESULTS BEYOND PEANO ARITHMETIC
Lee, Gyesik;

Abstract
We expose a pattern for establishing Friedman-Weiermann style independence results according to which there are thresholds of provability of some parameterized variants of well-partial-ordering. For this purpose, we investigate an ordinal notation system for $\small{{\vartheta}{\Omega}^{\omega}}$, the small Veblen ordinal, which is the proof-theoretic ordinal of the theory $\small{({\prod}{\frac{1}{2}}-BI)_0}$. We also show that it sometimes suffices to prove the independence w.r.t. PA in order to obtain the same kind of independence results w.r.t. a stronger theory such as $\small{({\prod}{\frac{1}{2}}-BI)_0}$.
Keywords
independence results;Peano arithmetic;Kruskal's theorem;
Language
English
Cited by
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