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  1. Strong downward Löwenheim–Skolem theorems for stationary logics, II: reflection down to the continuum.Sakaé Fuchino, André Ottenbreit Maschio Rodrigues & Hiroshi Sakai - 2021 - Archive for Mathematical Logic 60 (3):495-523.
    Continuing, we study the Strong Downward Löwenheim–Skolem Theorems of the stationary logic and their variations. In Fuchino et al. it has been shown that the SDLS for the ordinary stationary logic with weak second-order parameters \. This SDLS is shown to be equivalent to an internal version of the Diagonal Reflection Principle down to an internally stationary set of size \. We also consider a version of the stationary logic and show that the SDLS for this logic in internal interpretation (...)
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  • Towers and clubs.Pierre Matet - 2021 - Archive for Mathematical Logic 60 (6):683-719.
    We revisit several results concerning club principles and nonsaturation of the nonstationary ideal, attempting to improve them in various ways. So we typically deal with a ideal J extending the nonstationary ideal on a regular uncountable cardinal \, our goal being to witness the nonsaturation of J by the existence of towers ).
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