First-order limits, an analytical perspective

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• 作者：Jaroslav Ne&scaron ; etřil^a ; ^{nesetril@iuuk.mff.cuni.cz" class="auth_mail" title="E-mail the corresponding author} ; Patrice Ossona de Mendez^b ; ^c ; ^{pom@ehess.fr" class="auth_mail" title="E-mail the corresponding author}
• 刊名：European Journal of Combinatorics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：52
• 期：part_PB
• 页码：368-388
• 全文大小：733 K

文摘

In this paper we present a novel approach to graph (and structural) limits based on model theory and analysis. The role of Stone and Gelfand dualities is displayed prominently and leads to a general theory, which we believe is naturally emerging. This approach covers all the particular examples of structural convergence and it put the whole in new context. As an application, it leads to new intermediate examples of structural convergence and to a “grand conjecture” dealing with sparse graphs. We survey the recent developments.