Cores of countably categorical structures
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure has a core, i.e., an endomorphism such that the structure induced by its image is a core; moreover, the core is unique up to isomorphism. We prove that every ω -categorical structure has a core. Moreover, every ω-categorical structure is homomorphically equivalent to a model-complete core, which is unique up to isomorphism, and which is finite or ω -categorical. We discuss consequences for constraint satisfaction with ω-categorical templates.
Details
Original language | English |
---|---|
Pages (from-to) | 1–16 |
Journal | Logical methods in computer science |
Volume | 3 |
Issue number | 1 |
Publication status | Published - 25 Jan 2007 |
Peer-reviewed | Yes |
Externally published | Yes |
External IDs
Scopus | 76849101459 |
---|---|
ORCID | /0000-0001-8228-3611/work/142241158 |
Keywords
Keywords
- Constraint satisfaction, Cores, ω-categorical structures