Canonical forking in AECs

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• 作者：Will Boney^a ; ¹ ; ^{wboney@math.harvard.edu" class="auth_mail" title="E-mail the corresponding author} ; ; Rami Grossberg^b ; ^{rami@cmu.edu" class="auth_mail" title="E-mail the corresponding author} ; Alexei Kolesnikov^c ; ^{akolesnikov@towson.edu" class="auth_mail" title="E-mail the corresponding author} ; Sebastien Vasey^b ; ² ; ^{sebv@cmu.edu" class="auth_mail" title="E-mail the corresponding author} ;
• 关键词：03C48 ; 03C45 ; 03C52 ; 03C55
• 刊名：Annals of Pure and Applied Logic
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：167
• 期：7
• 页码：590-613
• 全文大小：553 K

文摘

Boney and Grossberg [7] proved that every nice AEC has an independence relation. We prove that this relation is unique: in any given AEC, there can exist at most one independence relation that satisfies existence, extension, uniqueness and local character. While doing this, we study more generally the properties of independence relations for AECs and also prove a canonicity result for Shelah's good frames. The usual tools of first-order logic (like the finite equivalence relation theorem or the type amalgamation theorem in simple theories) are not available in this context. In addition to the loss of the compactness theorem, we have the added difficulty of not being able to assume that types are sets of formulas. We work axiomatically and develop new tools to understand this general framework.