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Published November 2, 2025 | Version v1
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Partition-Dominating Sets: Rigged Partitions, Filters, Forcing, and Sphere Paradoxes (Preprint)

Authors/Creators

Description

Renamed from "Half-Dense Sets" for clarity. Pure ZFC proofs; no data.

Abstract

We define n-partition-dominating sets and prove their existence under precise cardinality hypotheses. We establish density, comeager properties, filter generation, and forcing preservation. Finally, we show that selector sets in the Hausdorff and Banach–Tarski paradoxes contain partition-dominating subsets, revealing a unified combinatorial structure.

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Half_Dense_Sets__Rigged_Partitions__Filters__Forcing__and_Sphere_Paradoxes__PUB_READY_ (1).pdf

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