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Abstract/Sommario: Introduction: sets and languages - The development of ZFC - The Lévy hierarchy and the reflection principle - Inaccessible and Mahlo cardinals - The constructible universe - Measurable cardinals - Trees and partition properties - Partition cardinals and model theory: Silver's results - Indescribable cardinals - Infinitary languages and large cardinals.

Abstract/Sommario: First order predicate calculus - Peano arithmetic - Second order systems and simple type theory - Infinitary logic - Consistency proofs - Some applications of consistency proofs.

Abstract/Sommario: Introduction - Formal systems - Epitheory - Lambda-Conversion - The Church-Rosser theorem - Intuitive theory of combinators - Synthetic theory of combinators - Logistic foundations - Introduction to illative combinatory logic - The basic theory of functionality - The stronger theories of functionality.

Abstract/Sommario: A proof of the relative consistency of the continuum hypothesis - Equivalences between Godel's definitions of constructibility - Concrete models of set theory - Independence of the axiom of choice from variants of the generalized continuum hypothesis - Ultraproducts and other methods of constructing models - Uniform extension operators for models and their applications - Representations of probabilities defined on first order languages - On Lowenheim-Skolem-Type insufficiencies of seco ...; [Leggi tutto...] A proof of the relative consistency of the continuum hypothesis - Equivalences between Godel's definitions of constructibility - Concrete models of set theory - Independence of the axiom of choice from variants of the generalized continuum hypothesis - Ultraproducts and other methods of constructing models - Uniform extension operators for models and their applications - Representations of probabilities defined on first order languages - On Lowenheim-Skolem-Type insufficiencies of second order logic - Some problems of definability in recursive function theory - Computable functionals of finite type I - Metarecursion theory - Recursively enumerable degrees and the degree less than 0 - Regressive isols - Arithmetic - Disjunction and existence in formalized intuitionistic analysis.

Abstract/Sommario: The frame of logic and class theory - The start of general set theory - Ordinals; natural numbers; finite sets - Transfinite recursion - Power; order; wellorder - The completing axioms - Analysis; cardinal arithmetic; abstract - Further strengthening of the axiom system.

Abstract/Sommario: The logic of scientific knowledge - Levels of knowledge and stages in the process of knowledge - Logical and physical implication - The deductive method as a problem of the logic of science - Probability logic and its role in scientific research - The basic forms and rules of inference by analogy - On the types of definition and their importance for science - Idealization as a method of scientific knowledge - The statistical interpretation of fact and the role of statistical methods in ...; [Leggi tutto...] The logic of scientific knowledge - Levels of knowledge and stages in the process of knowledge - Logical and physical implication - The deductive method as a problem of the logic of science - Probability logic and its role in scientific research - The basic forms and rules of inference by analogy - On the types of definition and their importance for science - Idealization as a method of scientific knowledge - The statistical interpretation of fact and the role of statistical methods in the structure of empirical knowledge.

Abstract/Sommario: The eminent philosopher of science Carl G. Hempel, Stuart Professor of Philosophy at Princeton University and a Past President of the American Philosophical Association, has had a long and distinguished academic career in the course of which he has been professorial mentor to some of America's most distinguished philosophers. This volume gathers together twelve original papers by Hempel's students and associates into a volume intended to do homage to Hempel on the occasion of his 65th ...; [Leggi tutto...] The eminent philosopher of science Carl G. Hempel, Stuart Professor of Philosophy at Princeton University and a Past President of the American Philosophical Association, has had a long and distinguished academic career in the course of which he has been professorial mentor to some of America's most distinguished philosophers. This volume gathers together twelve original papers by Hempel's students and associates into a volume intended to do homage to Hempel on the occasion of his 65th year in 1970. The papers are grouped around the unifying topic of Hempel's own interests in logic and philosophy of science, the great majority dealing with issues on inductive logic and the theory of scientific explanatio- problems to which Hempel has devoted the bulk of his outstandingly fruitful efforts. With the approach of 'Peter' Hempel's 65th birthday, an editorial committee sprang into being by an uncannily spontaneous process to prepare to commemorate this event with an appropriate Festschrift. The editors were pleased to receive unfailingly prompt and efficient coopera­ tion on the part of all contributors. The responsibility of seeing the work through the press was assumed by Nicholas Rescher. The editors are grateful to all concerned for their collaboration.

Abstract/Sommario: Methods based on the representation of the solution as an infinite series - The approximate solution of the integral equations of Fredholm - The method of nets - Variational methods - The conformal transformation of regions - Principles of the application of conformal transformation to the solution of the fundamental problems for canonical regions - Schwarz's method.