Journal of Mathematical Logic· 2026Q1
Symmetries of graphs and structures that fail to interpret a finite thing
- 1citations
- Q1SCImago
- 2026year
Short summary
Researchers identified new algebraic invariance properties for directed graphs that do not interpret every finite structure, with implications for constraint satisfaction problems.
AI-generated from the title and abstract; the full text is not read.
Key points
- Identified new algebraic invariance properties for directed graphs that do not interpret every finite structure.
- These properties are linked to the tractability of constraint satisfaction problems.
- New properties are established for infinite countably categorical graphs.
- A countably categorical hypergraph lacking essential algebraic invariance properties was constructed.
AI-generated from the title and abstract; the full text is not read.
Abstract
In this paper, we investigate structural implications arising from the condition that a given directed graph does not interpret, in the sense of primitive positive interpretation with parameters or orbits, every finite structure. Our results generalize several theorems from the literature and yield further algebraic invariance properties that must be satisfied in every such graph. Algebraic properties of this kind are tightly connected to the tractability of constraint satisfaction problems, and we obtain new such properties even for infinite countably categorical graphs. We balance these positive results by showing the existence of a countably categorical hypergraph that fails to interpret some finite structure, while still lacking some of the most essential algebraic invariance properties known to hold for finite structures.
The authors' abstract, as published at the source. Journal of Mathematical Logic, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics