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  1. A contribution to the end-extension problem and the Π1 conservativeness problem.Zofia Adamowicz - 1993 - Annals of Pure and Applied Logic 61 (1-2):3-48.
    We formulate a Π1 sentence τ which is a version of the Tableau consistency of GlΔ0. The sentence τ is true and is provable in GlΔ0 + exp. We construct a model M of GlΔ0+Ω1+τ+BGs1 which has no proper end-extension to a model of GlΔ0+Ω1+τ. Also we prove that GlΔ0+Ω1+τ is not Π1 conservative over GlΔ0+τ.
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