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A Model–Theoretic Approach to Proof Theory
This book presents a detailed treatment of ordinal combinatorics of large sets tailored for independence results. It uses model theoretic and combinatorial methods to obtain results in proof theory, such as incompleteness theorems or a description of the provably total functions of a theory. In the first chapter, the authors first discusses ordinal combinatorics of finite sets in the style of Ketonen and Solovay. This provides a background for an analysis of subsystems of Peano Arithmetic as well as for combinatorial independence results. Next, the volume examines a variety of proofs of Gödel's incompleteness theorems. The presented proofs differ strongly in nature. They show various aspect...
And Yet I Still Have Dreams
A brutally honest memoir of adolescence in the Warsaw ghetto and coming to terms with the memories years later
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.
Euphony and Logos
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Orders: Description and Roles
Orders: Description and Roles
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.
Statistical Inference
Use and misuse of statistics seems to be the signum temporis of past decades. But nowadays this practice seems slowly to be wearing away, and common sense and responsibility recapturing their position. It is our contention that little by little statistics should return to its starting point, i.e., to formalizing and analyzing empirical phenomena. This requires the reevalu ation of many traditions and the rejection of many myths. We hope that our book would go some way towards this aim. We show the sharp conflict between what is needed and what is feasible. Moreover, we show how slender are the links between theory and practice in statistical inference, links which are sometimes no more than ...
Paradoxes of Measures and Dimensions Originating in Felix Hausdorff's Ideas
In this book, many ideas by Felix Hausdorff are described and contemporary mathematical theories stemming from them are sketched.
The Structure of Models of Peano Arithmetic
Aimed at graduate students, research logicians and mathematicians, this much-awaited text covers over 40 years of work on relative classification theory for nonstandard models of arithmetic. The book covers basic isomorphism invariants: families of type realized in a model, lattices of elementary substructures and automorphism groups.
