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We consider the extent to which one can compute bounds on the rate of convergence of a sequence of ergodic averages. It is not difficult to construct an example of a computable Lebesgue measureâ€¦ (More)

In this paper we prove general logical metatheorems which state that for large classes of theorems and proofs in (nonlinear) functional analysis it is possible to extract from the proofs effectiveâ€¦ (More)

- Philipp Gerhardy
- CSL
- 2003

In [1, 2] Zhang shows how the complexity of cut elimination depends primarily on the nesting of quantifiers in cut formulas. By studying the role of contractions in cut elimination we can refine thatâ€¦ (More)

- Philipp Gerhardy, Ulrich Kohlenbach
- Ann. Pure Appl. Logic
- 2006

In [12], the second author obtained metatheorems for the extraction of effective (uniform) bounds from classical, prima facie nonconstructive proofs in functional analysis. These metatheorems for theâ€¦ (More)

In [J.Math.Anal.App.277(2003) 645-650], W.A.Kirk introduced the notion of asymptotic contractions and proved a fixed point theorem for such mappings. Using techniques from proof mining, we develop aâ€¦ (More)

- Philipp Gerhardy, Ulrich Kohlenbach
- Arch. Math. Log.
- 2005

Carrying out a suggestion by Kreisel, we adapt GÃ¶delâ€™s functional interpretation to ordinary first-order predicate logic(PL) and thus devise an algorithm to extract Herbrand terms from PL-proofs. Theâ€¦ (More)

- Philipp Gerhardy
- Notre Dame Journal of Formal Logic
- 2008

A famous theorem by van der Waerden states the following: Given any finite colouring of the integers, one colour contains arbitrarily long arithmetic progressions. Equivalently, for every q, k thereâ€¦ (More)

- R. M. Baltrusaitis, G. L. Cassiday, +6 authors Daniel Steck
- 2001

extensive-air-shower maxima as a function of atmospheric depth. This distribution has an exponential tail whose slope is Ã« = 72 Â± 9 g cm which implies that Ã³p-air= 530 Â± 66 mb. Using Glauber theoryâ€¦ (More)

- M. BALTRUSAITIS, G. L. CASSIDAY, +11 authors Daniel Steck
- 2001

During 1985 June, July, August, and October, small air showers from the direction of Cygnus X-3 were observed using the University of Utah Fly's Eye. Useful spectral information was obtained fromâ€¦ (More)

- Philipp Gerhardy
- 2007

Proof-theoretic aspects of obtaining a constructive version of the mean ergodic theorem â€“ p. 1/27 Introduction 'Proof mining' is the subfield of mathematical logic that is concerned with theâ€¦ (More)