On Some Infinitary Logics

2024/02/20 by Vaananen, Jouko, Velickovic, Boban
#03C55 #03C75 #03C95 #03Exx #FOS: Mathematics #Logic (math.LO) #Primary: 03Bxx

paper · doi:10.48550/arxiv.2402.13344

Abstract

We define a new class of infinitary logics \mathscr L¹_κ,α generalizing Shelah's logic \mathbb L¹_κ defined in \citeMR2869022. If κ=\beth_κ and α<κ is infinite then our logic coincides with \mathbb L¹_κ. We study the relation between these logics for different parameters κ and α. We give many examples of classes of structures that can or cannot be defined in these logics. Finally, we give a different version of Lindström's Theorem for \mathbb L¹_κ in terms of the ϕ-submodel relation.

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