Is there a set theoretic way to look at SQL? I have been learning about SQL and at times it feels like set theory.  A statement like SELECT * FROM myTable is like a set $\{ x: x \in \text{myTable} \}$.

A table could be defined as any subset of the Cartesian product.  We could define a table called zipcodes with a schema city STRING(30), state CHAR(2),  zip INTEGER(5)  then in set theory we could define the zipcodes stable as:
$$ zicodes \subseteq \text{cities} \times \text{states} \times \text{zips} \simeq \{a, \dots, Z\}^{30} \times \{a, \dots, Z\} \times \{1, \dots, 10^5\}$$
So any table is a subset of a cartesian product.

My theory has limitations, since you can't store all of $\mathbb{R}$ as a SQL database (e.g. by cantor diagonalization) since $|\mathbb{R}| &gt; |\mathbb{Z}|$ in cardinality.  

In any case, do any theories of SQL exist that compare it to set theory?
It is common wisdom that database field is firmly grounded in the two math disciplines: predicate logic and set theory. However, this is very fuzzy observation, and reality is more subtle.

The structure of the basic building block - relation - is described in set language, but that's about it. This is not really very insightful, because the whole mathematics is written in set language. The fact that probably caught your attention is that the foundation of SQL - relational algebra - has distinct Boolean flavor.

Please also note that SQL actually operates not with relations but multirelations which are bags(multisets) of tuples(rows). Therefore, its algebra is not a [boolean] algebra of sets. There were various attempts at rigorous theory of multirelations, with provenance semiring being the most recent development