Partitions of Baire space into compact sets

2023/12/15 by Vera Fischer, Fischer, Vera, Lukas Schembecker +1
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2312.09994

openalex publication_date 2023/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Under CH we construct a partition of Baire space into compact sets, which is indestructible by countably supported iteration and product of Sacks forcing of any length, answering a question of Newelski. Further, we present an in-depth isomorphism-of-names argument for spec(\mathfraka_T) = \ℵ₁, \mathfrakc\ in the product-Sacks model. Finally, we prove that Shelah's ultrapower model for the consistency of \mathfrakd < \mathfraka also satisfies \mathfraka = \mathfraka_T. Thus, consistently ℵ₁ < \mathfrakd < \mathfraka = \mathfraka_T holds relative to a measurable.

Related

• Partitions of 2^ω and completely ultrametrizable spaces
• The κ-Fréchet-Urysohn property for C_p(X) is equivalent to Baireness of B₁(X)
• On the first Banach problem, concerning condensations of absolute κ-Borel sets onto compacta
• Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces. II
• A T₀-Compactification Of A Tychonoff Space Using The Rings Of Baire One Functions