PREDICATIVITY THROUGH TRANSFINITE REFLECTION

Predicativity beyond Γ0

We reevaluate the claim that predicative reasoning (given the natural numbers) is limited by the Feferman-Schütte ordinal Γ 0. First we comprehensively criticize the arguments that have been offered in support of this position. Then we analyze predicativism from first principles and develop a general method for accessing ordinals which is predicatively valid according to this analysis. We find ...

Predicativity beyond Γ0

We reevaluate the claim that predicative reasoning (given the natural numbers) is limited by the Feferman-Schütte ordinal Γ 0. First we comprehensively criticize the arguments that have been offered in support of this position. Then we analyze predicativism from first principles and develop a general method for accessing ordinals which is predicatively valid according to this analysis. We find ...

Transfinite Equations in Transfinite Strings

Transfinite Diameter

The transfinite diameter is a way of quantifying the size of compact sets in Euclidean space. This quantity is related to the Hausdorff dimension and the Lebesgue measure, but gives a slightly different perspective on the set than either of those do. In this paper, we introduce the transfinite diameter, and outline some attempts to calculate this quantity for three sets in R. For z1, z2, . . . ...

on “ Predicativity as a philosophical position ”

In his provocative article for this issue, Geoffrey Hellman has astutely attacked the philosophical grounds for predicativity from several angles. Though I am not now nor never have been a predicativist, I have to admit to being a sympathizer since I am an avowed anti-platonist, at least insofar as set theory is concerned, and I grant the natural numbers a position of primacy in our mathematica...