Chicagoan Frank Gallagher is the proud single dad of six smart, industrious, independent kids, who without him would be... perhaps better off. When Frank's not at the bar spending what little money they have, he's passed out on the floor. But the kids have found ways to grow up in spite of him. They may not be like any family you know, but they make no apologies for being exactly who they are.

This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel’s classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel’s second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo’s axioms, containing a presentation of Gödel’s constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers.

The homecoming show was a rousing success, predominantly featuring long electronic interpretations of songs from Autobahn. Perhaps the finest show of the entire world tour, the show was also broadcast for transmission on local radio and is now presented here in full for the first time. Featuring the group at their zenith as they began to truly establish themselves as one of the most important electronic groups in existence, the show serves as a historical and cultural document of a band in their ascendancy. Bonus tracks here feature from Kraftwerk’s show on 28th February 1976 in Paris, France, shortly after the release of the equally successful Radio-Activity in late 1975, demonstrating the early sonic evolution of the classic Hütter-Schneider-Bartos-Flür lineup and their rapidly developing mastery of the electronic format in those early years.

This book provides a cross-disciplinary overview of permafrost and the carbon cycle by providing an introduction into the geographical distribution of permafrost, with a focus on the distribution of permafrost and its soil carbon reservoirs. The chapters explain the basic physical properties and processes of permafrost soils: ice, mineral and organic components, and how these interact with climate, vegetation and geomorphological processes. In particular, the book covers the role of the large quantities of ice in many permafrost soils which are crucial to understanding carbon cycle processes.

This book constitutes the refereed conference proceedings of the 14th International Conference on Advances in Computer Entertainment Technology, ACE 2017, held in London, UK, in December 2017.
The 59 full papers presented were selected from a total of 229 submissions.
ACE is by nature a multi-disciplinary conference, therefore attracting people across a wide spectrum of interests and disciplines including computer science, design, arts, sociology, anthropology, psychology, and marketing. The main goal is to stimulate discussion in the development of new and compelling entertainment computing and interactive art concepts and applications.

This book constitutes the refereed proceedings of the 6th Annual Smart City 360° Summit. Due to COVID-19 pandemic the conference was held virtually.