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Woher wissen wir was wahr ist? Wofür brauchen wir mathematische Beweise? Was hat es mit Gödels berühmten Unvollständigkeitssätzen auf sich? In diesem Sachbuch tauchen wir ein in die Aussagekraft mathematischer Systeme und lernen ihre prinzipiellen Grenzen kennen. Nicht...
This festschrift honors Johann A. Makowsky on the occasion of his 75th birthday. Gathering 24 research articles authored by scientific companions, friends, and colleagues, it covers a broad variety of areas to which Johann A. Makowsky made significant contributions...
This book provides the reader with a comprehensive account of the contributions of Pythagoras to mathematics and philosophy, using them as a starting point to compare pre-Pythagorean accomplishments with the myriad mathematical developments that followed. It begins with...
Classical logic – which studies the structural features of purported claims of fact – and modal logic – which studies relations of necessity and possibility – are different but complementary areas of logical thought. In this lively and accessible textbook, Adam...
The theory of definable equivalence relations has been a vibrant area of research in descriptive set theory for the past three decades. It serves as a foundation of a theory of complexity of classification problems in mathematics and is further motivated by the study of...
Propositiones ad acuendos juvenes (“Problems to Sharpen the Young”) is a ninth-century book written by medieval teacher and scholar Alcuin of York. Today, it has become one of the foundational texts in what is commonly called recreational mathematics. The book has been...
Developing the theory up to the current state-of-the art, this book studies the minimal model of the Largest Suslin Axiom (LSA), which is one of the most important determinacy axioms and features prominently in Hugh Woodin's foundational framework known as the Ultimate...
What follows from what, and how do we make statements (whether true or false) about which inferences are correct? In this book, Edwin Mares provides a new philosophical, semantical and historical analysis of and justification for the relevant logic of entailment. In the...
How should we treat the liar and kindred paradoxes? A Theory of Truth argues that we should diverge from classical logic, and presents a new formal theory of truth. The theory does not incorporate contradictions and is not substructural, but deviates from classical...
Erleben Sie das Wiedererwachen des universitären Lebens nach 1918 aus der Sicht eines Betroffenen. Tauchen Sie ein in die Erziehungs- und Sozialgeschichte der Mathematik zur Zeit der Weimarer Republik und erfahren aus der Perspektive eines jungen Autors das Aufstreben...
Kurt Gödel (1906-1978) gained world-wide fame by his incompleteness theorem of 1931. Later, he set as his aim to solve what are known as Hilbert's first and second problems, namely Cantor's continuum hypothesis about the cardinality of real numbers, and secondly the...
Emphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof. The material revolves around possible strategies to approaching a problem without classifying 'types of proofs' or providing proof...
»Philosophy of Mathematics« is understood, in this book, as an effort to clarify such questions that mathematics itself raises but cannot answer with its own methods. These include, for example, questions about the ontological status of mathematical objects (e.g., what...
Constructive mathematics – mathematics in which 'there exists' always means 'we can construct' – is enjoying a renaissance. fifty years on from Bishop's groundbreaking account of constructive analysis, constructive mathematics has spread out to touch almost all areas of...
The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs, Fifth Edition provides basic logic of mathematical proofs and how they work.The book offers techniques for both reading and writing proofs, discusses techniques in proving if/then statements by...
This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include...
This book proves some important new theorems in the theory of canonical inner models for large cardinal hypotheses, a topic of central importance in modern set theory. In particular, the author 'completes' the theory of Fine Structure and Iteration Trees (FSIT) by...
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and...
Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes...
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