Definition:Operation Compatible with Set Equivalence

Definition

Let $F$ be a (unary) operation which can be applied to sets.

Then $F$ is compatible with set equivalence if and only if:

$F \sqbrk A = F \sqbrk B \iff A \sim B$

where:

$A$ and $B$ are arbitrary sets

$F \sqbrk A$ denotes the image of $A$ under $F$

$\sim$ denotes set equivalence.

Sources

• 1999: András Hajnal and Peter Hamburger: Set Theory ... (previous) ... (next): $2$. Definition of Equivalence. The Concept of Cardinality. The Axiom of Choice: Definition $2.2$