Some family feuds don't die; they bleed so deep into the soil they grow roots.This one is ripping the country apart, but only those embroiled in it know it's being fought. Half dead from her last estrus and desperate to save her homeland, Eve makes the difficult journey to the Capital of the New South in an attempt to court the only Alpha she thinks might be honorable. She offers him herself, her nest, and her submission if he allows her to get to know him first, gives her a semblance of choice, and at least listens to the plight of her people.Only The Alpha isn't much of a listener, and he neglects to read the document he signs out of frustration to get his hands on the exotic beauty in front of him. After taking Eve as his, he finds that holding an Omega who moves like smoke isn't as easy as he thought.Contract broken, Eve lies, steals, and takes what she needs to gain the strength needed to fight a war none of them can afford to lose. The Alpha may not know it, but the fate of the New South lies in her hands.***The Omega Rule is a dystopian, m/f, HEA, Omegaverse novel and contains elements of dubious consent. If such material offends you, please do not purchase. 18 and Over. ***

The Omega-Theory: A New Physics of Earthquakes, Second Edition offers a unifying, mathematical framework to describe and answer the most pressing and unexamined dilemmas of earthquake sequences. Those in the fields of seismology and geology are currently faced with a vast and complex mathematical structure, involving many new, natural laws and theorems. This book interprets this structure as a new physical theory and paradigm, helping users understand the tectonic and seismic processes within the Earth. As such, it is an essential resource for future researchers in the fields of structural geology, physics of the Earth, and seismology. In the last decades, generations of seismologists, geophysicists, and geologists have accumulated enough knowledge and information to allow for the reformulation and solution of this essential problem. Hence, this book provides a great resource for researchers and professionals. - Brings together twenty years of research in the field of geophysics and attacks the problem within the framework of the Cosserat continuum theory - Heavily tested on tens of natural examples and numerical tests - Includes 350 color figures and graphs - Spans across many fields of theoretical physics and geology, such as plate tectonics, synchronization of chaotic systems, solitons and fractals, mathematical set theory, and quantum mechanics

Abstract: "An important technique for investigating derivability in formal systems of arithmetic has been to embed such systems into semi- formal systems with the [omega]-rule. This paper exploits this notion within the domain of automated theorem-proving and discusses the implementation of such a proof environment, namely the CORE system which implements a version of the primitive recursive [omega]-rule. This involves providing an appropriate representation for infinite proofs, and a means of verifying properties of such objects. By means of the CORE system, from a finite number of instances a conjecture for a proof of the universally quantified formula is automatically derived by an inductive inference algorithm, and checked for correctness. In addition, candidates for cut formulae may be generated by an explanation-based learning algorithm. This is an alternative approach to reasoning about inductively defined domains from traditional structural induction, which may sometimes be more intuitive."

Evan Ryder returns to uncover an international conspiracy against American democracy in a white-knuckle new thriller by New York Times bestselling author, Eric Van Lustbader. Evan Ryder was once a field agent for a black-ops arm of the Department of Defense. Now she works for Parachute, a cutting-edge quantum-computing firm whose private espionage network exceeds any government spy agency. But her mission remains the same: seek out and destroy Omega, a fanatical global cult intent on destroying democracy. The fight against Omega has already cost Evan dearly but she will not stop until she has torn out the conspiracy by its roots, no matter the risk. In Omega Rules, the assassination of a Parachute agent in Vienna sets Evan on a dangerous, world-wide hunt for answers and on a collision course with forces so powerful they may be beyond her abilities to annihilate. Once again Lustbader delivers a prescient exploration of the political and ideological forces that are wreaking havoc on the stability of the Western world and its struggling democracies. At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.

This volume presents a novel approach to set theory that is entirely operational. This approach avoids the existential axioms associated with traditional Zermelo-Fraenkel set theory, and provides both a foundation for set theory and a practical approach to learning the subject. It is written at the professional/graduate student level, and will be of interest to mathematical logicians, philosophers of mathematics and students of theoretical computer science.

What follows from what, and how do we make statements (whether true or false) about which inferences are correct? In this book, Edwin Mares provides a new philosophical, semantical and historical analysis of and justification for the relevant logic of entailment. In the first half of the book he examines some key ideas in the historical development of the logic of entailment, looking in particular at the notion 'is derivable from' and at how symbolic logic has attempted to capture this notion. In the second half of the book he develops his own theory connecting ideas from the traditions in mathematical logic with some ideas in the philosophy of science. The book's fresh and original perspective on the logic of entailment will be valuable for all who want to know more about the historical and philosophical origins of modern symbolic logic.

What is the source of logical and mathematical truth? This volume revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. In Shadows of Syntax, Jared Warren offers the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. He argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims. In Part I, Warren explains exactly what conventionalism amounts to and what linguistic conventions are. Part II develops an unrestricted inferentialist theory of the meanings of logical constants that leads to logical conventionalism. This conventionalist theory is elaborated in discussions of logical pluralism, the epistemology of logic, and of the influential objections that led to the historical demise of conventionalism. Part III aims to extend conventionalism from logic to mathematics. Unlike logic, mathematics involves both ontological commitments and a rich notion of truth that cannot be generated by any algorithmic process. To address these issues Warren develops conventionalist-friendly but independently plausible theories of both metaontology and mathematical truth. Finally, Part IV steps back to address big picture worries and meta-worries about conventionalism. This book develops and defends a unified theory of logic and mathematics according to which logical and mathematical truths are reflections of our linguistic rules, mere shadows of syntax.