# Extend Lowenheim's decidability result to fragment of second-order logic

Since relational monadic first-order logic has finite model property, its SAT problem is decidable. In H.Behmann's paper, he extended this result to fragment of SOL where all predicates, free and bound are monadic. I am not familiar with SOL and his paper was not written in English. Can you give me any hint to prove this result?

Thanks!

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Several sources on line describe it briefly, saying it is proved by quantifier elimination. For anyone who wants to look into this, the article is Behmann "Beiträge zur Algebra der Logik, insbesondere zum Entscheidungsproblem" Mathematische Annalen 86 (1922): 163-229. gdz.sub.uni-goettingen.de/dms/load/img/?PPN=GDZPPN002268752 –  Colin McLarty Sep 21 '13 at 13:22