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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2021 Volume 18, Issue 1, Pages 433–455 (Mi semr1371)

Mathematical logic, algebra and number theory

Independence and simplicity in Jonsson theories with abstract geometry

A. R. Yeshkeyev, M. T. Kassymetova, O. I. Ulbrikht

Buketov Karaganda University, 28, Universitetskaya str., Karaganda, 100028, Kazakhstan

Abstract: The concepts of forking and independence are examined in the framework of the study of Jonsson theories and the fixed Jonsson spectrum. The axiomatically given property of nonforking satisfies the classical notion of nonforking in the sense of S. Shelah and the approach to this concept by Laskar-Poizat. On this basis, the simplicity of the Jonsson theory is determined and the Jonsson analog of the Kim-Pillay theorem is given. Abstract pregeometry on definable subsets of the Jonsson theory's semantic model is defined. The properties of Morley rank and degree for definable subsets of the semantic model are considered. A criterion of uncountable categoricity for the hereditary Jonsson theory in the language of central types is proved.

Keywords: Jonsson theory, existentially closed model, Morley rank, cosemanticness, Jonsson spectrum, Jonsson set, a fragment of Jonsson set, Jonsson independence, Jonsson nonforking, Jonsson simplicity, central type, strong minimality, pregeometry, modular geometry.

UDC: 510.67

MSC: 03C60, 03C68, 03C10

Received December 30, 2019, published April 20, 2021

Language: English

DOI: 10.33048/semi.2021.18.030



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