FRIEDMAN-WEIERMANN STYLE INDEPENDENCE RESULTS BEYOND PEANO ARITHMETIC
Gyesik Lee · Journal of the Korean Mathematical Society · 2014
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 $({\prod}{\frac{1}{2}}-BI)_0$ .