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New Ramsey Classes from Old

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arxiv 1204.3258 v2 pith:ACP37JTC submitted 2012-04-15 math.LO math.CO

Manuel Bodirsky This is my paper
classification math.LOmath.CO
keywords ramseyclassesfinitesigmastructuresthenwedgewhose
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Let C_1 and C_2 be strong amalgamation classes of finite structures, with disjoint finite signatures sigma and tau. Then C_1 wedge C_2 denotes the class of all finite (sigma cup tau)-structures whose sigma-reduct is from C_1 and whose tau-reduct is from C_2. We prove that when C_1 and C_2 are Ramsey, then C_1 wedge C_2 is also Ramsey. We also discuss variations of this statement, and give several examples of new Ramsey classes derived from those general results.

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  1. Taking model-complete cores

    math.LO 2025-12 conditional novelty 8.0 of 10

    Core companions preserve stability, NIP, simplicity, and NSOP_k, but the classes of structures interpretable over (N;=) and (Q;<) are not closed under taking core companions.

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