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#

Sets

**Definition 3.1**

*a*

**pre-ordered**set is a set with the property that, between any two objects there is at most one arrow. This entails that there exists a binary relation R between the objects of the pre-ordered set such that the following holds:- aRa
**reflexivity**

- if aRb and bRc then aRc
**transitivity**

**Definition 3.2**

*a*

**poset**is a pre-ordered set with the extra property of being antisymmetric:

Cecilia Flori 2007-01-02