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In Memory of Solomon Marcus: A Journey Through Mathematical Logic and Foundations

Cooper Bell

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Published in Mathematics Almost Everywhere: In Memory Of Solomon Marcus (Mathematical Logic And Foundat)

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Solomon Marcus (1925-2016) was one of the most influential mathematicians of the twentieth century. He made significant contributions to mathematical logic, foundations of mathematics, computer science, and semiotics. His work has had a profound impact on these fields, and he is considered to be one of the founders of modern mathematical logic.

This book is a collection of commemorative essays in honor of Solomon Marcus. The essays were written by some of the world's leading experts in mathematical logic and foundations of mathematics, and they explore Marcus' work and its impact on these fields.

The essays in this volume are divided into four parts:

Mathematics Almost Everywhere: In Memory Of Solomon Marcus (Mathematical Logic and Foundat)

by Harry McCallion

4.5 out of 5

Language	:	English
File size	:	12421 KB
Text-to-Speech	:	Enabled
Screen Reader	:	Supported
Enhanced typesetting	:	Enabled
Print length	:	252 pages

Part I: Mathematical Logic
Part II: Foundations of Mathematics
Part III: Computer Science
Part IV: Semiotics

Each part contains essays that explore Marcus' work in that particular field. The essays are written in a clear and accessible style, and they are suitable for readers with a variety of backgrounds.

The essays in Part I explore Marcus' work in mathematical logic. Marcus was one of the leading figures in the development of mathematical logic in the twentieth century. He made significant contributions to the fields of model theory, set theory, and recursion theory.

One of Marcus' most important contributions to mathematical logic was his work on the theory of models. A model is a mathematical structure that satisfies a set of axioms. Marcus developed new methods for constructing and classifying models, and he used these methods to solve a number of important problems in mathematical logic.

Marcus also made significant contributions to set theory. He developed new methods for proving the independence of certain axioms of set theory. He also showed that there are models of set theory that are not well-founded. This result has had a profound impact on the foundations of mathematics.

Finally, Marcus made important contributions to recursion theory. He developed new methods for proving the undecidability of certain problems in recursion theory. He also showed that there are problems in recursion theory that are undecidable even if we allow the use of additional axioms.

The essays in Part I provide a comprehensive overview of Marcus' work in mathematical logic. They show that Marcus was one of the leading figures in the development of this field in the twentieth century.

The essays in Part II explore Marcus' work in foundations of mathematics. Marcus was one of the leading figures in the development of foundations of mathematics in the twentieth century. He made significant contributions to the fields of set theory, category theory, and proof theory.

One of Marcus' most important contributions to foundations of mathematics was his work on set theory. He developed new methods for proving the independence of certain axioms of set theory. He also showed that there are models of set theory that are not well-founded. This result has had a profound impact on the foundations of mathematics.

Marcus also made significant contributions to category theory. He developed new methods for constructing and classifying categories. He also showed that there are deep connections between category theory and other areas of mathematics, such as algebraic topology and algebraic geometry.

Finally, Marcus made important contributions to proof theory. He developed new methods for proving the consistency of certain axiomatic systems. He also showed that there are axiomatic systems that are consistent but incomplete. This result has had a profound impact on the foundations of mathematics.

The essays in Part II provide a comprehensive overview of Marcus' work in foundations of mathematics. They show that Marcus was one of the leading figures in the development of this field in the twentieth century.

The essays in Part III explore Marcus' work in computer science. Marcus was one of the leading figures in the development of computer science in the twentieth century. He made significant contributions to the fields of automata theory, formal languages, and artificial intelligence.

One of Marcus' most important contributions to computer science was his work on automata theory. He developed new methods for constructing and classifying automata. He also showed that there are deep connections between automata theory and other areas of mathematics, such as group theory and algebra.

Marcus also made significant contributions to formal languages.

Mathematics Almost Everywhere: In Memory Of Solomon Marcus (Mathematical Logic and Foundat)

by Harry McCallion

4.5 out of 5