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    If higher levels Σ^1_n yield genuinely new interpolation ... — Carmelics
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    Challenges→The expressive hierarchy Σ^1_n ∪ Π^1_n of second-order logic already has its full power concentrated at the first level Σ^1_1 ∪ Π^1_1 with respect to Löwenheim and Hanf numbers

    If higher levels Σ^1_n yield genuinely new interpolation and preservation failures, the claim that expressive power is 'concentrated' at level one is operationally misleading.

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