Absolute Values -- Valuations -- Extension of Valuations -- Henselian Fields -- Structure Theory -- Applications of Valuation Theory.Absolute values and their completions -like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valu…
Propositions and Truth Assignments -- Formal Propositional Calculus -- Predicates and Models -- Formal Predicate Calculus -- Some Uses of Compactness.At the heart of the justification for the reasoning used in modern mathematics lies the completeness theorem for predicate calculus. This unique textbook covers two entirely different ways of looking at such reasoning. Topics include: - the repres…
The Evolution of Type Theory until the 1940s -- Prehistory -- Type theory in Principia Mathematica -- Deramification -- Propositions as Types, Pure Type Systems, AUTOMATH -- Propositions as Types and Pure Type Systems -- The pre-PAT RTT and STT in PAT-style -- A Correspondence between RTT and the system Nuprl -- Automath -- Extensions of Pure Type Systems -- Pure Type Systems with definitions -…
Universal Logic: Frameworks and Structures -- From Consequence Operator to Universal Logic: A Survey of General Abstract Logic -- Abstract Model Theory as a Framework for Universal Logic -- A Topological Approach to Universal Logic: Model-Theoretical Abstract Logics -- Selfextensional Logics with Implication -- Logic without Self-Deductibility -- Identity and Nature of Logical Structures -- Equ…
Problems and Tricks -- Number Theory -- Some Applications of Elementary Number Theory -- Ideas and Theories -- Induction and Recursion -- Arithmetic of algebraic numbers -- Arithmetic of algebraic varieties -- Zeta Functions and Modular Forms -- Fermat’s Last Theorem and Families of Modular Forms -- Analogies and Visions -- Introductory survey to part III: motivations and description -- Arake…
Infinite Galois Theory and Profinite Groups -- Valuations and Linear Disjointness -- Algebraic Function Fields of One Variable -- The Riemann Hypothesis for Function Fields -- Plane Curves -- The Chebotarev Density Theorem -- Ultraproducts -- Decision Procedures -- Algebraically Closed Fields -- Elements of Algebraic Geometry -- Pseudo Algebraically Closed Fields -- Hilbertian Fields -- The Cla…
A Fundamental Theorem -- Topics in Algebra -- Some Quadratic Problems -- The Genus of an Algebraic Curve -- Miscellany."... The exposition is not only clear, it is friendly, philosophical, and considerate even to the most naive or inexperienced reader. And it proves that the philosophical orientation of an author really can make a big difference. The mathematical content is intensely classical.…
Chapter 1. Introduction: Context and Connections -- Chapter 2. Alex C. Michalos: Pioneer of Quality of Life and Social Indicators; Bruno Zumbo -- Chapter 3. An Interview with Alex C. Michalos; Dan Weijers -- Chapter 4. The Best Teacher I Ever Had Was J. Coert Rylaarsdam -- Chapter 5. The Case for Atheism, Notes for a Discussion; Alex C. Michalos -- Chapter 6. Logic, Philosophy of Science and th…
Chapter 1: Logics for Normative Supervenience (Antonino Rotolo) -- Chapter 2: Propositional and Doxastic Justification: Their Relationship and a Questionable Supervenience Claim (Giorgio Volpe) -- Chapter 3: Moral Properties: Some Epistemological, Ontological, and Normative Dimensions (Robert Audi) -- Chapter 4: Reasons and Supervenience (Daniel Laurier) -- Chapter 5: The Dubious Moral Superve…
Semantic Foundations -- Retracing the Semantics of CSP -- Seeing Beyond Divergence -- Refinement and Simulation -- Process Algebra: A Unifying Approach -- Linking Theories of Concurrency -- Hardware Synthesis -- CSP, occam and Transputers -- Models for Data-Flow Sequential Processes -- Implementation of Handshake Components -- Transactions -- A Trace Semantics for Long-Running Transactions -- P…