Definition:Quasi-Reflexive Relation/Class Theory

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