Local Resistance in Early Medieval Chinese Historiography and the Problem of Religious Overinterpretation

Official Chinese historiography is a treasure trove of information on local resistance to the centralised empire in early medieval China (third to sixth century). Sinologists specialised in the study of Chinese religions commonly reconstruct the religious history of the era by interpreting some of these data. In the process, however, the primary purpose of the historiography of local resistance is often overlooked, and historical interpretation easily becomes ‘overinterpretation’—that is, ‘fabricating false intensity’ and ‘seeing intensity everywhere’, as French historian Paul Veyne proposed to define the term. Focusing on a cluster of historical anecdotes collected in the standard histories of the four centuries under consideration, this study discusses the supposedly ‘religious’ nature of some of the data they contain

Semirigid equivalence relation of a finite set

13ppInternational audienceA system $R$ of equivalence relations on a set $A$ (with at least $3$ elements) is \emph{semirigid} if only the trivial operations (that is the projections and constant functions) preserve all members of $R$. To a system $R$ of equivalence relations we associate a graph $G_R$. We observe that if $R$ is semirigid then the graph $G_R$ is $2$-connected. We show that the converse holds if all the members of $R$ are atoms of the lattice $E$ of equivalence relations on $A$. We present a notion of graphical composition of semirigid systems and show that it preserves semirigidity

Hereditary rigidity, separation and density In memory of Professor I.G. Rosenberg

International audienceWe continue the investigation of systems of hereditarily rigid relations started in Couceiro, Haddad, Pouzet and Schölzel [1]. We observe that on a set V with m elements, there is a hereditarily rigid set R made of n tournaments if and only if m(m − 1) ≤ 2 n. We ask if the same inequality holds when the tournaments are replaced by linear orders. This problem has an equivalent formulation in terms of separation of linear orders. Let h Lin (m) be the least cardinal n such that there is a family R of n linear orders on an m-element set V such that any two distinct ordered pairs of distinct elements of V are separated by some member of R, then ⌈log 2 (m(m − 1))⌉ ≤ h Lin (m) with equality if m ≤ 7. We ask whether the equality holds for every m. We prove that h Lin (m+1) ≤ h Lin (m)+1. If V is infinite, we show that h Lin (m) = ℵ0 for m ≤ 2 ℵ 0. More generally, we prove that the two equalities h Lin (m) = log2(m) = d(Lin(V)) hold, where log 2 (m) is the least cardinal µ such that m ≤ 2 µ , and d(Lin(V)) is the topological density of the set Lin(V) of linear orders on V (viewed as a subset of the power set P(V × V) equipped with the product topology). These equalities follow from the Generalized Continuum Hypothesis, but we do not know whether they hold without any set theoretical hypothesis

Semirigid Systems of Equivalence Relations.

International audienceA system \\textbackslashmathcal M\ of equivalence relations on a set \E\ is \textbackslashemph\semirigid\ if only the identity and constant functions preserve all members of \\textbackslashmathcal M\. We construct semirigid systems of three equivalence relations. Our construction leads to the examples given by Z\textbackslash'adori in 1983 and to many others and also extends to some infinite cardinalities. As a consequence, we show that on every set of at most continuum cardinality distinct from \2\ and \4\ there exists a semirigid system of three equivalence relations

Semirigid systems of three equivalence relations

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