1
$\begingroup$

If $R(x,z_1,\dots, z_n)\subset \mathbb{N}^{n+1}$ is a relation, then is the thing $(\forall y < x) R(y,z_1,\dots, z_n)$ a relation? I can't see how to interpret it as a set (relations are sets), so it doesn't look to me that it's a relation. What is it then?

$\endgroup$
1
  • $\begingroup$ It looks like a statement (that for any $y$ less than $x$ in some sense, $𝑅(𝑦,𝑧_1,\ldots,𝑧_𝑛)$ holds. $\endgroup$ Nov 6 '19 at 22:28
0
$\begingroup$

This is a formula, which defines a relation. Namely the relation $$\{(x,z_1,\dots,z_n)\in N^{n+1}\mid (y,z_1,\dots,z_n)\in R \text{ for all }y<x\}.$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.