Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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FRIEDMAN-WEIERMANN STYLE INDEPENDENCE RESULTS BEYOND PEANO ARITHMETIC

  • Lee, Gyesik (Department of Computer Science and Web Information Engineering Hankyong National University)
  • Received : 2013.07.30
  • Accepted : 2013.12.03
  • Published : 2014.03.01
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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 ${\vartheta}{\Omega}^{\omega}$, the small Veblen ordinal, which is the proof-theoretic ordinal of the theory $({\prod}{\frac{1}{2}}-BI)_0$. 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 $({\prod}{\frac{1}{2}}-BI)_0$.

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References

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