A Simplified Proof of the 0–1 Law for Existential Second‐Order Ackermann Sentences

Mathematical Logic Quarterly 43 (3):413-418 (1997)
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Abstract

Recently we gave a finitistic proof of the 0–1 law for ∑11 (Ackermann) sentences, which relied as much as possible on the original argument of Kolaitis and Vardi. Here we present another version of our proof which, on the contrary, is self‐contained. Finitism allows us to use the beautiful probabilistic argument of Kolaitis and Vardi in a simple and intuitive way. Consequently, we obtain a shorter proof.

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10.1002/malq.19970430314

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Probabilities on finite models.Ronald Fagin - 1976 - Journal of Symbolic Logic 41 (1):50-58.

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