Work

Epic math battle of history: Grothendieck vs Nikodym

Year: 2024

Type: article

Abstract: We define a σ -centered notion of forcing that forces the existence of a Boolean algebra with the Grothendieck property and without the Nikodym property. In particular, the existence of such an algebra is consistent with the negation of the continuum hypothesis. The algebra we construct consists of Borel subsets of the Cantor set and has cardinality ω 1 . We also show how to apply our method to streamline Talagrand's construction of such an algebra under the continuum hypothesis.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2024.110757

Authors: Damian Głodkowski, Agnieszka Widz

Institutions: Institute of Mathematics, University of Warsaw, Polish Academy of Sciences, Lodz University of Technology

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,670

Funders: Fields Institute for Research in Mathematical Sciences, Division of Mathematical Sciences