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Logic of Mathematics
A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems: * Gödel's theorems of completeness and incompleteness * The independence of Goodstein's theorem from Peano arithmetic * Tarski's theorem on real closed fields * Matiyasevich's theorem on diophantine formulas Logic o...
Metamereology
Our aim in this book is not simply to provide an introduction to the topic of mereology but also to undertake a thorough analysis of it. Hence its name: "Metamereology". Mereology arose as a theory of collective sets. It was formulated by the Polish logician Stanisław Leśniewski. Collective sets are certain wholes composed of parts. In general, the concept of a collective set can be defined with the help of the relation "is a part of" and mereology may therefore be considered as a theory of the relation of part to the whole'' (from the Greek: meros, "part'').
Andrzej Mostowski and Foundational Studies
Andrzej Mostowski was one of the leading 20th century logicians. This volume examines his legacy, devoted both to his scientific heritage and to the memory of him as a great researcher, teacher, organizer of science and person. It includes the bibliography of Mostowski's writings.
The Epistemic Lightness of Truth
This volume explores the deflationary claim of the innocence of truth, taking into account recent results on axiomatic truth theories.
Foundational Studies
Foundational Studies
Emergence and Convergence
Two problems continually arise in the sciences and humanities, according to Mario Bunge: parts and wholes and the origin of novelty. In Emergence and Convergence, he works to address these problems, as well as that of systems and their emergent properties, as exemplified by the synthesis of molecules, the creation of ideas, and social inventions. Along the way, Bunge examines further topical problems, such as the search for the mechanisms underlying observable facts, the limitations of both individualism and holism, the reach of reduction, the abuses of Darwinism, the rational choice-hermeneutics feud, the modularity of the brain vs. the unity of the mind, the cluster of concepts around 'may...
Trends in Logic
In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica. The volume features a series of papers by distinguished scholars reflecting both the aim and scope of this journal for symbolic logic.
Foundational Studies Selected Works
Foundational Studies Selected Works
Set Theory
During the past 25 years, set theory has developed in several interesting directions. The most outstanding results cover the application of sophisticated techniques to problems in analysis, topology, infinitary combinatorics and other areas of mathematics. This book contains a selection of contributions, some of which are expository in nature, embracing various aspects of the latest developments. Amongst topics treated are forcing axioms and their applications, combinatorial principles used to construct models, and a variety of other set theoretical tools including inner models, partitions and trees. Audience: This book will be of interest to graduate students and researchers in foundational problems of mathematics.
