 A fundamental theme in proof theory (in particular in the branch of this discipline known as ordinal analysis) is the classification of theories by means of transfinite ordinals which measure their "consistency strength" and "computational power".  These ordinals give an indication of how strong a theory is, and therefore offer a way of comparing different theories. For example, the ordinal \(\varepsilon_0\) is the proof-theoretic ordinal of Peano Arithmetic, and is much smaller than the ordinal \(\Gamma_0\), usually referred to as "the limit of predicativity"   (see section 1.3 above).   This is indicative that there are predicatively acceptable theories which are much stronger than Peano Arithmetic. 