Abstract
Many results concerning the equivalence between a syntactic form of formulas and a model theoretic conditions are proven directly without using any form of a continuum hypothesis. In particular, it is demonstrated that any reduced product sentence is equivalent to a Horn sentence. Moreover, in any first order language without equality one now has that a reduced product sentence is equivalent to a Horn sentence and any sentence is equivalent to a Boolean combination of Horn sentences.
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Nelson, G.C. Preservation Theorems Without Continuum Hypothesis. Studia Logica 60, 343–355 (1998). https://doi.org/10.1023/A:1005028511181
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DOI: https://doi.org/10.1023/A:1005028511181