A Universe with large Continuum, global Σ-Uniformization and a projective Well-Order of its Reals

2025/06/14 by Stefan Hoffelner, Hoffelner, Stefan
Physics and Astronomy · #Cosmology and Gravitation Theories #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2506.12393

Abstract

We construct a model in which the continuum has size κ for a regular cardinal κ and in which the Σ¹_n-uniformization property holds simultaneously for every n ≥ 2. Additionally this model has a Δ¹₃- definable well-order of its reals.

Citations

• Forcing the Π¹_n-Uniformization Property
• Forcing Axioms, the Uniformization and the Basis Property

Related

• A Universe with a Δ¹_n-definable well-order of the reals, CH and Π¹_n-Uniformization
• The global Σ¹_n+1-Uniformization Property and BPFA
• Forcing the Π¹_n-Uniformization Property
• Forcing upper Σ-uniformization in the presence of lower Π-reduction or uniformization
• A model with everything except for a well-ordering of the reals