Table of Contents

Additive number systems: Background from analysis Counting functions, fundamental identities Density and partition sets The case $rho = 1$ The case $0 < rho < 1$ Monadic second-order limit laws Multiplicative number systems: Background from analysis Counting functions and fundamental identities Density and partition sets The case $alpha = 0$ The case $0 < alpha < infty$ First-order limit laws Appendix A. Formal power series Appendix B. Refined counting Appendix C. Consequences of $delta(mathsf P) = 0$ Appendix D. On the monotonicity of $a(n)$ when $p(n) leq 1$ Appendix E. Results of Woods Bibliography Symbol index Subject index.