Year: 2024
Type: preprint
Abstract: We define a new class of infinitary logics $\mathscr L^1_{κ,α}$ generalizing Shelah's logic $\mathbb L^1_κ$ defined in \cite{MR2869022}. If $κ=\beth_κ$ and $α<κ$ is infinite then our logic coincides with $\mathbb L^1_κ$. 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 $\mathbb L^1_κ$ in terms of the $ϕ$-submodel relation.
Source: arXiv (Cornell University)
Authors: Vaananen, Jouko, Velickovic, Boban
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4392083020