{"paper":{"title":"Almost disjoint refinements and mixing reals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Barnab\\'as Farkas, Yurii Khomskii, Zolt\\'an Vidny\\'anszky","submitted_at":"2015-10-19T21:43:29Z","abstract_excerpt":"We investigate families of subsets of $\\omega$ with almost disjoint refinements in the classical case as well as with respect to given ideals on $\\omega$. More precisely, we study the following topics and questions:\n  1) Examples of projective ideals.\n  2) We prove the following generalization of a result due to J. Brendle: If $V\\subseteq W$ are transitive models, $\\omega_1^W\\subseteq V$, $\\mathcal{P}(\\omega)\\cap V\\not = \\mathcal{P}(\\omega)\\cap W$, and $\\mathcal{I}$ is an analytic or coanalytic ideal coded in $V$, then there is an $\\mathcal{I}$-almost disjoint refinement ($\\mathcal{I}$-ADR) of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05699","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}