Combinatorial properties and dependent choice in symmetric extensions based on Lévy collapse

Banerjee, Amitayu (2022) Combinatorial properties and dependent choice in symmetric extensions based on Lévy collapse. ARCHIVE FOR MATHEMATICAL LOGIC, Publis. ISSN 0933-5846

Preview

Text 1903.05945v3.pdf Download (432kB) | Preview

Abstract

We work with symmetric extensions based on Lévy collapse and extend a few results of Apter, Cody, and Koepke. We prove a conjecture of Dimitriou from her Ph.D. thesis. We also observe that if V is a model of ZFC, then DC<κ can be preserved in the symmetric extension of V in terms of symmetric system ⟨ P, G, F⟩ , if P is κ-distributive and F is κ-complete. Further we observe that if δ< κ and V is a model of ZF+ DCδ, then DCδ can be preserved in the symmetric extension of V in terms of symmetric system ⟨ P, G, F⟩ , if P is (δ+ 1)-strategically closed and F is κ-complete. © 2022, The Author(s).

Actions (login required)

Edit Item