{"paper":{"title":"Combinatorial properties of Hechler forcing","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Haim Judah, J\\\"org Brendle, Saharon Shelah","submitted_at":"1992-11-03T00:00:00Z","abstract_excerpt":"In this work we use a notion of rank first introduced by James Baumgartner and Peter Dordal and later developed independently by the third author to show that adding a Hechler real has strong combinatorial consequences.\n  We prove:\n 1) assuming omega_1^V = omega_1^L, there is no real in V[d] which is eventually different from the reals in L[d], where d is Hechler over V;\n 2) adding one Hechler real makes the invariants on the left-hand side of Cicho'n's diagram equal omega_1 and those on the right-hand side equal 2^omega and produces a maximal almost disjoint family of subsets of omega of size"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9211202","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"}