An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.

Alberta's oil sands represent a vast and untapped oil reserve that could reasonably supply all of Canada's energy needs for the next 475 years. With an estimated 300 billion barrels of recoverable oil at stake, the quest to develop this natural resource has been undertaken by many powerful actors, both nationally and internationally. Using research that integrates the economic, political, scientific, and business factors that have been influential in discovering and developing the sands, this book provides a comprehensive history of the oil sands project and a window on the nature of the complex relationships between industry, government, and transnational players. This book is the first comprehensive volume that examines the origins and development of the oil sands industry over the last century.

New York Times Bestseller Picture this. Your hair is a mess and you feel like a nut. You open your Drybar book and you feel better already! The Drybar Guide to Good Hair for All is the ultimate handbook for at-home hairstyling. Author Alli Webb, a long-time stylist and life-long curly hair girl, founded Drybar in 2010 as an affordable luxury—offering women a great blowout in a beautiful and fun atmosphere. Today, there are more than 60 Drybars across the country, with more opening every day. Drybar’s book makes it easy for women to get the Drybar look at home. Webb shares her tried and true tricks and tips in three in-depth sections featuring more than 100 style-inspiration photograph and step-by-step tutorials. Bright, upbeat, and loaded with style and substance, this book will give readers everywhere a good hair day at home!

A textbook on the semantics, proof theory, and metatheory of first-order logic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. It is based on the Open Logic project, and available for free download at slc.openlogicproject.org.

From the magisterial to the mundane, achievements play a role in the best kind of human life, and many people think that they are of such importance that they are worth pursuing at the expense of serious sacrifices. Yet for all that, no philosophers have devoted more than a few short passages to discerning what makes achievements valuable, or even what makes something an achievement to begin with. Gwen Bradford presents the first systematic account of what achievements are, and what it is about them that makes them worth doing. It turns out that more things count as achievements than we might have thought, and that what makes them valuable isn't something we usually think of as good. It turns out that difficulty, perhaps surprisingly, plays a central part in characterizing achievements and their value: achievements are worth the effort. But just what does it mean for something to be difficult, and why is it valuable? A thorough analysis of the nature of difficulty is given, and ultimately, the best account of the value of achievements taps into perfectionist axiology. But not just any perfectionist theory of value will do, and in this book we see a new perfectionist theory developed that succeeds in capturing the value of achievement better than its predecessors.

Calgary, Alberta is a culturally diverse urban metropolis. Sprawling and car-dependent, fast-growing and affluent, it is dominated by the fossil fuel industry. For 30 years, Calgary has struggled to turn sustainability rhetoric into reality. Sustainability Matters is the story of Calgary's setbacks and successes on the path toward sustainability. Chronicling two decades of public conversations, political debate, urban policy and planning, and scholarly discovery, it is both a fascinating case study and an accessible introduction to the theory and practice of urban sustainability. A clear-eyed view of the struggles of turning knowledge into action, this book illuminates the places where theory and reality converge and presents an approach to municipal development, planning, and governance that takes seriously the urgent need to address climate change and injustice. Addressing a wide variety of topics and themes, including energy, diversity, economic development, and ecological health, Sustainability Matters is both a critique of current practice and a vision for the future that uses the city of Calgary as a microcosm to address issues faced by cities around the world. This is essential reading not only for every Calgarian working for a vibrant and sustainable future, but for all those interested in in the future of cities in a post-carbon world.

"The inaugural title in the new, Open Access series BSPS Open, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. Which that is, and its extent, is determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference."--

A textbook on modal and other intensional logics. It covers normal modal logics, relational semantics, axiomatic and tableaux proof systems, intuitionistic logic, and counterfactual conditionals. It is based on the Open Logic Project and available for free download at openlogicproject.org.

Titus Maccius Plautus' career is on the decline. Once renound for bringing Greek comedies to the Roman world, now he struggles to stage a single play. Unlucky with money and unlucky in love, Plautus faces the world with wry dignity. This could be the performance that brings back fame and fortune, or the one that ends it all. Engaging, thoughtful, and funny, The Comedian dives into the rough and tumble world of arts in its infancy. Clem Martini draws on his talent and experience to bring to life the signs and sounds of a world where playwrights suffered and succeeded--but mostly suffered.