Аннотация:
The original Goodstein principle is a number-theoretic statement known to be independent from PA. It proceeds by writing numbers in so-called hereditary exponential form, then applying various operations to produce a finite (but very long) sequence. In recent work with T. Arai and S. Wainer, we have shown that a similar process based on the Ackermann function leads to independence results for ATR0. In this talk we discuss how modifications in the representation of such numbers can lead to independence results for theories of intermediate strength.