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Universal Graphs with Forbidden Subgraphs and Algebraic Closure |
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| Authors: | Gregory Cherlin Saharon Shelah Niandong Shi |
| Affiliation: | aDepartment of Mathematics, Rutgers University, Busch Campus, New Brunswick, New Jersey, 08903;bDepartment of Mathematics, Hebrew University, Jerusalem, Israel;cRutgers University, New Brunswick, New Jersey, 08903;dDepartment of Mathematics, East Stroudsburg University, East Stroudsburg, Pennsylvania, 18301, f1 |
| Abstract: | We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an associated “algebraic closure” operator. The main applications are new examples of universal graphs with forbidden subgraphs and simplified treatments of some previously known cases. |
| Keywords: | universal graph forbidden subgraph algebraic closure model theory 0-categoricity model completeness existential completeness |
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