An interpretation of the Sigma-2 fragment of classical Analysis in System T

Danko Ilik (1)

1 PARSIFAL - Proof search and reasoning with logic specifications

We show that it is possible to define a realizability interpretation for the Σ 2 -fragment of classical Analysis using Gödel's System T only. This supplements a previous result of Schwichtenberg regarding bar recursion at types 0 and 1 by showing how to avoid using bar recursion altogether. Our result is proved via a conservative extension of System T with an operator for composable continuations from the theory of programming languages due to Danvy and Filinski. The fragment of Analysis is therefore essentially con-structive, even in presence of the full Axiom of Choice schema: Weak Church's Rule holds of it in spite of the fact that it is strong enough to refute the formal arithmetical version of Church's Thesis.

Mots clés: Axiom of Choice; Modified realizability; Gödel's System T; Delimited control operators; Existence Property; Church's Thesis

Domaines: Logique [math.LO]; Logique en informatique [cs.LO]; Langage de programmation [cs.PL]

Danko Ilik. An interpretation of the Sigma-2 fragment of classical Analysis in System T. 2014. ⟨hal-01092411⟩