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+Π⁰_∞‐BCT is conservative over RCA₀ with respect to the set of formulae in the form ∃!Xφ(X), where φ is arithmetical. We also consider the conservation of Π⁰_0∞‐BCT over Σ^b₁‐NIA+∇^b₁‐CA.