2. "Analysis in J_2". This is an expository paper in which I explain how core mathematics, particularly abstract analysis, can be developed within a concrete countable set J_2 (the second set in Jensen's constructible hierarchy). The implication, well-known to proof theorists but probably not to most mainstream mathematicians, is that ordinary mathematical practice does not require an enigmatic metaphysical universe of sets. I go further and argue that J_2 is a superior setting for normal mathematics because it is free of irrelevant set-theoretic pathologies and permits stronger formulations of existence results. In LaTex, DVI, PS, PDF.

3. "Predicativity beyond Gamma_0". We reevaluate the claim that predicative reasoning (given the natural numbers) is limited by the Feferman-Schutte ordinal Gamma_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 that the Veblen ordinal \phi_{\Omega^\omega}(0), and larger ordinals, are predicatively provable. In LaTex, DVI, PS, PDF.

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Solomon Feferman has given a detailed critique of the paper "Predicativity beyond Gamma_0", and I have written a comprehensive response to his critique.

Solomon Feferman's response (posted here with permission)
My response to Solomon Feferman's letter

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Last modified September 11, 2005
nweaver@math