INDEPENDENCE AND SIMPLICITY IN JONSSON THEORIES WITH ABSTRACT GEOMETRY
Yeshkeyev A.R. Kassymetova M.T. Ulbrikht O.I.
2021Sobolev Institute of Mathematics
Siberian Electronic Mathematical Reports
2021#18Issue 1433 - 455 pp.
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.
a fragment of Jonsson set , central type , cosemanticness , existentially closed model , Jonsson independence , Jonsson nonforking , Jonsson set , Jonsson simplicity , Jonsson spectrum , Jonsson theory , modular geometry , Morley rank , pregeometry , strong minimality
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