Math @ Duke

Publications [#348694] of Benjamin Rossman
Papers Published
 Rossman, B, Homomorphism preservation theorems,
Journal of the Acm, vol. 55 no. 3
(July, 2008) [doi]
(last updated on 2022/05/19)
Abstract: The homomorphism preservation theorem (h.p.t.), a result in classical model theory, states that a firstorder formula is preserved under homomorphisms on all structures (finite and infinite) if and only if it is equivalent to an existentialpositive formula. Answering a longstanding question in finite model theory, we prove that the h.p.t. remains valid when restricted to finite structures (unlike many other classical preservation theorems, including the o  Tarski theorem and Lyndon's positivity theorem). Applications of this result extend to constraint satisfaction problems and to database theory via a correspondence between existentialpositive formulas and unions of conjunctive queries. A further result of this article strengthens the classical h.p.t.: we show that a firstorder formula is preserved under homomorphisms on all structures if and only if it is equivalent to an existentialpositive formula of equal quantifierrank. © 2008 ACM.


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