This appears in Tarski's book Cardinal Algebras as Theorem 2.28, called Interpolation Theorem, and the statement of the theorem is as follows:
If $n\leq\infty,\ p\leq\infty$, such that $a_i\leq b_j$ for $i< n$ and $j < p$, then there is an element $c$ such that $a_i\leq c\leq b_j$ for every $i < n$ and $j < p$.
The theorem appears on page 27. The full citation is given below, one can also read about it on MathSciNet.
Tarski, Alfred. Cardinal Algebras. With an Appendix: Cardinal Products of Isomorphism Types, by Bjarni Jónsson and Alfred Tarski. Oxford University Press, New York, N. Y., 1949. xii+326 pp.