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Preservation and decomposition theorems for bounded degree structures

Frederik Harwath ; Lucas Heimberg ; Nicole Schweikardt.

We provide elementary algorithms for two preservation theorems for first-order sentences (FO) on the class \^ad of all finite structures of degree at most d: For each FO-sentence that is preserved under extensions (homomorphisms) on \^ad, a \^ad-equivalent existential (existential-positive)&nbsp;[&hellip;]

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On the locality of arb-invariant first-order formulas with modulo counting quantifiers

Frederik Harwath ; Nicole Schweikardt.

We study Gaifman locality and Hanf locality of an extension of first-order logic with modulo p counting quantifiers (FO+MOD_p, for short) with arbitrary numerical predicates. We require that the validity of formulas is independent of the particular interpretation of the numerical predicates and&nbsp;[&hellip;]

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