Abstract: Unlike the case of WKL0, there do not seem to be many principles equivalent to 
over RCA0. There is, however, a whole world of principles, particularly combinatorial ones, below 
(i.e., provable in 
) in the reverse mathematical universe. We have already discussed 
and COH. In this chapter, we consider a few more, to illustrate some of the workings of this world below 
. We begin by focusing on a principle called ADS, as an extended example. We then briefly mention several other combinatorial principles provable from 
. Finally, we discuss some basic theorems that come from what would seem like quite a different area of mathematics, namely model theory, but nevertheless also inhabit this part of the reverse mathematical universe. For the most part, the level of detail in this chapter will be lower than in our long case study of 
; much more information can be found in the cited papers, among several others. The literature of this area of research continues to expand, so searching for recent papers and preprints is likely to prove rewarding. It is also a useful exercise to fill out the diagrams in the previous chapter with the principles mentioned below, either by hand or using the Reverse Mathematics Zoo mentioned in the previous chapter; several of the papers cited in this chapter also contain such extended diagrams.
