More Set-theory around the weak Freese-Nation property

1996/05/03 by Sakaé Fuchino, Fuchino, Sakae, Lajos Soukup +1 · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.math/9605208

openalex publication_date 1996/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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(χ). 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. A typical application of this characterization shows that under 2^ℵ₀

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