Definition:Quasi-Reflexive Relation/Class Theory
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Definition
Let $V$ be a basic universe
Let $\RR \subseteq V \times V$ be a relation.
$\RR$ is quasi-reflexive if and only if:
- $\forall x \in \Field \RR: \tuple {x, x} \in \RR$
where $\Field \RR$ denotes the field of $\RR$.
Also known as
Some sources use this definition to define a reflexive relation on a basic universe $V$.
Such treatments do not distinguish between a relation which is reflexive on its field and one which is reflexive on an arbitrary subclass of $V$
Also see
- Results about quasi-reflexive relations can be found here.
Sources
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text I$ -- Superinduction and Well Ordering: $\S 1$ Introduction to well ordering