This volume makes the basic facts about admissible sets accessible to logic students and specialists alike.

Addresses various ways computability and theoretical computer science enable scientists and philosophers to deal with mathematical and real-world issues. This book covers problems related to logic, mathematics, physical processes, real computation and learning theory.

In this book, Yurii L. Ershov posits the view that computability-in the broadest sense-can be regarded as the Sigma-definability in the suitable sets. He presents a new approach to providing the Gödel incompleteness theorem based on systematic use of the formulas with the restricted quantifiers. The volume also includes a novel exposition on the foundations of the theory of admissible sets with urelements, using the Gandy theorem throughout the theory's development. Other topics discussed are forcing, Sigma-definability, dynamic logic, and Sigma-predicates of finite types.

This volume showcases the best of recent research in the philosophy of science. A compilation of papers presented at the EPSA 13, it explores a broad distribution of topics such as causation, truthlikeness, scientific representation, gender-specific medicine, laws of nature, science funding and the wisdom of crowds. Papers are organised into headings which form the structure of the book. Readers will find that it covers several major fields within the philosophy of science, from general philosophy of science to the more specific philosophy of physics, philosophy of chemistry, philosophy of the life sciences, philosophy of psychology, and philosophy of the social sciences and humanities, amongst others. This volume provides an excellent overview of the state of the art in the philosophy of science, as practiced in different European countries and beyond. ​It will appeal to researchers with an interest in the philosophical underpinnings of their own discipline, and to philosophers who wish to explore the latest work on the themes explored.

This book discusses the econometric foundations of structural vector autoregressive modeling, as used in empirical macroeconomics, finance, and related fields.

Tenascin, a recently characterized extracellular matrix (ECM) protein which is expressed during embryonic and fetal development, wound healing and various benign and malignant tumors (but highly restricted in normal adult tissues) is believed to affect a number of cellular functions such as cellular growth, differentiation, adhesion and motility. It has been extensively studied in recent years to elucidate cellular phenomena that are associated with development, tissue regeneration and neoplastic growth and behavior. It may be a potential target in the treatment of cancers and other disorders. This book focuses mainly on tissue expression and the poorly known biological role of this ECM protein.

Fundamentals of Generalized Recursion Theory

Chemical Process Structures and Information Flows focuses on the role of computers in the understanding of chemical processes, including the use of simulation and optimization in computational problems. The book first underscores graphs and digraphs and pipeline networks. Discussions focus on cutsets and connectivity, directed graphs, trees and circuits, matrix representation of digraphs and graphs, reachability matrix, alternative problem formulations and specifications, and steady state conditions in cyclic networks. The manuscript also ponders on computation sequence in process flowsheet calculations and sparse matrix computation. The publication examines scheduling and design of batch plants, including scheduling of products and operations, characteristics of batch processes, branch and bound methods, and multipurpose batch plants. The text also elaborates on observability and redundancy and process data reconciliation and rectification. The manuscript is a valuable reference for chemical engineering students and readers interested in chemical processes and information flow.

Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods – some old, some new – that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students and a source of interesting new approaches for researchers in computability theory and related areas.