On homomorphism-homogeneous point-line geometries

• Autorzy: Jungabel Ėva

Identyfikatory

DOI

10.4467/20842589RM.19.007.10655

• Języki publikacji: EN

Abstrakty

EN

A relational structure is homomorphism-homogeneous if every homomorphism between finite substructures extends to an endomorphism of the structure. A point-line geometry is a non-empty set of elements called points, together with a collection of subsets, called lines, in a way that every line contains at least two points and any pair of points is contained in at most one line. A line which contains more than two points is called a regular line. Point-line geometries can alternatively be formalised as relational structures. We establish a correspondence between the point-line geometries investigated in this paper and the firstorder structures with a single ternary relation L satisfying certain axioms (i.e. that the class of point-line geometries corresponds to a subclass of 3-uniform hypergraphs). We characterise the homomorphism-homogeneous point-line geometries with two regular non-intersecting lines. Homomorphism-homogeneous pointline geometries containing two regular intersecting lines have already been classified by Mašulović.

Słowa kluczowe

EN

homomorphism-homogeneous; point-line geometry; first-order structure

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2019
• Tom: Vol. 54
• Strony: 101--119
• Opis fizyczny: Bibliogr. 19 poz., rys.

Twórcy

autor

Jungabel Ėva

• Mathematical Institute Ëotvös Loránd University Pázmány Péter sétány 1/C, 1117 Budapest, Hungary

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).