Number Theoretic Density and Logical Limit Laws
Stanley N. Burris · Mathematical surveys and monographs · 2000
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.