Amalgamation is PSPACE-hard

08/01/2021

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by   Manuel Bodirsky, et al.

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The finite models of a universal sentence Φ in a finite relational signature are the age of a homogeneous structure if and only if Φ has the amalgamation property. We prove that the computational problem whether a given universal sentence Φ has the amalgamation property is PSPACE-hard, even if Φ is additionally Horn and the signature of Φ only contains relation symbols of arity at most three. The decidability of the problem remains open.