 The natural numbers have a very rich structure. \(P\omega\) is the power set of the set of natural numbers and it is at the core of the model bearing the same label. Every natural number has a unique representation in base \(2\). (E.g., \(7_{10}\) is \(111\), that is, \(7=1\cdot2^2+1\cdot2^1+1\cdot 2^0=4+2+1\).) Each binary representation is of the form