Some More Conservation Results on the Baire Category Theorem

In this paper, we generalize a result of Brown and Simpson [1] to prove that RCA0+Π∞-BCT is conservative over RCA0 with respect to the set of formulae in the form ∃!X φ(X), where φ is arithmetical. We also consider the conservation of Π∞-BCT over Σ1-NIA+∇1-CA. Mathematics Subject Classification: 03F35, 03F60.