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## Section: New Results

### Interpretation of the Sigma-2-classical Axiom of Choice in System T

Participant : Danko Ilik.

Updating previous work, we showed that one can develop a realizability interpretation for the ${\Sigma }_{2}^{0}$-fragment of classical Analysis in System T only [36] .

This is known to be possible, in principle, by a 1979 result of Schwichtenberg. However, up to day no method that avoids both bar recursion (Spector) and control operators (Krivine) has been known. In fact, we propose to treat control operators as a meta-mathematical technique, rather than to have them in the language of realizers as classical realizability does; we provide a formal proof in Agda that control operators can be completely normalized away from System T while preserving essential equations. [15]