Proof Mining - Mathematics, Algorithms and Proofs
Proof Mining - Mathematics, Algorithms and Proofs
Proof Mining - Mathematics, Algorithms and Proofs
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<strong>Proof</strong> <strong>Mining</strong><br />
COROLLARY 17 (K.,Trans.AMS,2005)<br />
If A ω [X, d, W ] proves<br />
∀x ∈ P ∀y ∈ K∀z X , f X→X (f n.e. ∧ F ix(f) = ∅ → ∃v IN C∃)<br />
then there is a computable functional Φ(fx, b) s.t. for all<br />
x ∈ P, fx representative of x, b ∈ IN<br />
∀y ∈ K∀z ∈ X∀f : X → X(f n.e. → ∃v ≤ Φ(fx, b) C∃)<br />
holds in any b-bounded hyperbolic space (X, d, W ).<br />
Next Lecture: Much refined metatheorems for unbounded<br />
spaces (with P. Gerhardy)!<br />
Ulrich Kohlenbach 22