Abstract
A partial Lindenbaum algebra Γ A {\Gamma ^A} , where A A is a theory extending Peano arithmetic and Γ ∈ { Π n , Σ n } \Gamma \in \{ {\Pi _n},{\Sigma _n}\} , is the full Lindenbaum algebra for A A restricted to sentences in A A provably equivalent to Γ n {\Gamma _n} -sentences. Using a new result on pairs of partially conservative sentences, we show that Π n A \Pi _n^A and Σ n A \Sigma _n^A are not isomorphic.
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