The  Sandwich Theorems  proved in this paper give a new method to show that the partition function $a(n)$ of a partition identity $$ {\bf A}(x) \ :=\ \sum_{n=0}^\infty a(n)x^n\ =\  \prod_{n=1}^\infty (1-x^n)^{-p(n)} $$ satisfies the condition  RT $_1$ $$ \lim_{n\rightarrow \infty}{a(n-1)\over a(n)} \ =\ 1\,. $$ This leads to numerous examples of naturally occuring  classes of relational structures  whose finite members enjoy a logical 0–1 law.
['Jason P. Bell', 'Stanley Burris']
Partition Identities I: Sandwich Theorems and Logical 0–1 Laws