Abstract
A structure of finite signature is constructed so that: for all existential formulas ∃y⃗ φ(x⃗,y⃗) and for all tuples of elements ⃗ of the same length as the tuple x⃗, one can decide in a quadratic time depending only on the length of the formula, if ∃y⃗ φ(u⃗,y⃗) holds in the structure. In other words, the structure satisfies the relativized model-theoretic version of P=NP in the sense of [4]. This is a model-theoretical approach to results of Hemmerling and Gaßner.
Citation
Mihai Prunescu. "Structure with fast elimination of quantifiers." J. Symbolic Logic 71 (1) 321 - 328, March 2006. https://doi.org/10.2178/jsl/1140641177
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