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arXiv · 1505.02691

Hereditarily rigid relations

Miguel Couceiro·Lucien Haddad·Maurice Pouzet·Karsten Schölzel
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Abstract

An $h$-ary relation $\r$ on a finite set $A$ is said to be \emph{hereditarily rigid} if the unary partial functions on $A$ that preserve $\r$ are the subfunctions of the identity map or of constant maps. A family of relations ${\mathcal F}$ is said to be \emph{hereditarily strongly rigid} if the partial functions on $A$ that preserve every $\r \in {\mathcal F}$ are the subfunctions of projections or constant functions. In this paper we show that hereditarily rigid relations exist and we give a lower bound on their arities. We also prove that no finite hereditarily strongly rigid families of relations exist and we also construct an infinite hereditarily strongly rigid family of relations.

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Miguel Couceiro, Lucien Haddad, Maurice Pouzet, Karsten Schölzel. 2015-05-11. Hereditarily rigid relations. https://arxiv.org/abs/1505.02691

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