Generic stability, forking, and {thorn}-forking

Darío García, Alf Onshuus, Alexander Usvyatsov

Research output: Contribution to journalArticlepeer-review


Abstract notions of "smallness" are among the most important tools that model theory offers for the analysis of arbitrary structures. The two most useful notions of this kind are forking (which is closely related to certain measure zero ideals) and thorn-forking (which generalizes the usual topological dimension). Under certain mild assumptions, forking is the finest notion of smallness, whereas thorn-forking is the coarsest. In this paper we study forking and thorn-forking, restricting ourselves to the class of generically stable types. Our main conclusion is that in this context these two notions coincide. We explore some applications of this equivalence.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalTransactions of the American Mathematical Society
Issue number1
StatePublished - 2012
Externally publishedYes


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