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We study sigma-ideals and regularity properties related to the "filter-Laver" and "dual-filter-Laver" forcing partial orders. An important innovation which enables this study is a dichotomy theorem proved recently by Miller .  Arnold Miller, "Hechler and Laver Trees", Preprint 2012 (arXiv:1204.5198 [math.LO]).arXiv:1612.04170v1 fatcat:t4pqg3xqcrb5phzwtjegslnezy