Sorry if this is a very basic question. I've just been reading some papers where they define a series of relations $\langle R_1, R_2 . . . \rangle$ as an $\omega$ sequence, and I wasn't sure what it meant.
Is it something to do with the natural numbers? Is there anything special about calling it an $\omega$ sequence, or would people understand $\langle R_1, R_2 . . \rangle$ in the same way without it?
Thanks
They just mean that the sequence has indices $1, 2, 3, \ldots$, which they think of as the ordinal $\omega$. More generally, if the indices came from some ordered set $A$ instead of from $\omega$, they might call the sequence an $A$-sequence. For example, if we had an uncountable "sequence" $\langle R_i : i \in \omega_1\rangle$ this would be called an $\omega_1$-sequence.
By default, a "sequence" is finite or an $\omega$-sequence - the term "$\omega$-sequence" is relatively specialized, usually only used in areas close to set theory.