Proof Mining - Mathematics, Algorithms and Proofs
Proof Mining - Mathematics, Algorithms and Proofs
Proof Mining - Mathematics, Algorithms and Proofs
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>Proof</strong> <strong>Mining</strong><br />
The semi-classical case<br />
Consider the ituitionistic version BAi of BA.<br />
AC = full axiom of choice in all types<br />
CA¬ : ∃Φ∀x ρ (Φ(x) =0 0 ↔ ¬A(x)) A <strong>and</strong> ρ arbitrary.<br />
Observation: CA¬ implies WKL (<strong>and</strong> even UWKL) <strong>and</strong> the law<br />
of exluded middle for negated (<strong>and</strong> for ∃-free) formulas.<br />
Ulrich Kohlenbach 23