I'm totally lost about what parameters are in Set Theory. I've been looking through a bunch of books but none explicitly state what they are, only how they are used in formulas to make sets. Can someone please explain this idea?
2026-04-06 11:36:05.1775475365
What are Parameters in Set Theory
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A "parameter" (in what I assume is the context you have in mind) is just a specific set that is plugged in for a variable in a formula. For instance, the axiom schema of separation says that if $A$ and $Y_1,\dots,Y_n$ are sets and $\varphi(x,y_1,\dots,y_n)$ is a formula in the language of set theory (whose free variables are $x,y_1,\dots,y_n$), then there exists a set $B$ such that for all $z$, $$z\in B \leftrightarrow(z\in A\wedge\varphi(z,Y_1,\dots,Y_n)).$$ In this context, we refer to the sets $Y_1,\dots,Y_n$ as "parameters" which are being used in the formula $\varphi$ to define the set $Z$.