Work

The gluing property

Year: 2024

Type: article

Abstract: We introduce a new compactness principle which we call the gluing property. For a measurable cardinal [Formula: see text] and a cardinal [Formula: see text], we say that [Formula: see text] has the [Formula: see text]-gluing property if every sequence of [Formula: see text]-many [Formula: see text]-complete ultrafilters on [Formula: see text] can be glued into an extender. We show that every [Formula: see text]-compact cardinal has the [Formula: see text]-gluing property, yet non-necessarily the [Formula: see text]-gluing property. Finally, we compute the exact consistency strength for [Formula: see text] to have the [Formula: see text]-gluing property — this being [Formula: see text].

Source: Journal of Mathematical Logic

DOI: 10.1142/s0219061324500302

Authors: Yair Hayut, Alejandro Poveda

Institutions: Hebrew University of Jerusalem, Harvard University

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Harvard University, Hebrew University of Jerusalem, Israel Science Foundation, Division of Mathematical Sciences

Award: G2022801861