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A Simplified Proof of the 0–1 Law for Existential Second‐Order Ackermann Sentences
Author(s) -
Lacoste Thierry
Publication year - 1997
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19970430314
Subject(s) - ackermann function , argument (complex analysis) , simple (philosophy) , probabilistic logic , order (exchange) , mathematics , direct proof , computer science , mathematical economics , calculus (dental) , discrete mathematics , epistemology , philosophy , statistics , medicine , biochemistry , inverse , chemistry , finance , dentistry , economics , geometry
Recently we gave a finitistic proof of the 0–1 law for ∑ 1 1 (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.