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  1. Feferman–Vaught Decompositions for Prefix Classes of First Order Logic.Abhisekh Sankaran - 2023 - Journal of Logic, Language and Information 32 (1):147-174.
    The Feferman–Vaught theorem provides a way of evaluating a first order sentence \(\varphi \) on a disjoint union of structures by producing a decomposition of \(\varphi \) into sentences which can be evaluated on the individual structures and the results of these evaluations combined using a propositional formula. This decomposition can in general be non-elementarily larger than \(\varphi \). We introduce a “tree” generalization of the prenex normal form (PNF) for first order sentences, and show that for an input sentence (...)
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