{"paper":{"title":"More Set-theory around the weak Freese-Nation property","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Lajos Soukup, Sakae Fuchino","submitted_at":"1996-05-03T00:00:00Z","abstract_excerpt":"In this paper, we introduce a very weak square principle which is even weaker than the similar principle introduced by Foreman and Magidor.  A characterization of this principle is given in term of sequences of elementary submodels of H(\\chi). This is used in turn to prove a characterization of kappa-Freese-Nation property under the very weak square principle and a weak variant of the Singular Cardinals Hypothesis.\n  A typical application of this characterization shows that under 2^{\\aleph_0}<\\aleph_\\omega and our very weak square for \\aleph_\\omega, the partial ordering [omega_\\omega]^{<\\omega"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9605208","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"}