Diagonalization in Formal Mathematics

ISBN-13: 9783658291105 / Angielski / Miękka / 2020 / 89 str.

Paulo Guilherme Santos

Spis treści

Diagonalization in Mathematics.- Diagonalization Lemma.- Fixed Point Theorems.- Paradoxes: Liar, Yablo’s Paradox, Curry’s Paradox.

O autorze

Paulo Guilherme Santos is currently a PhD student at FCT, Universidade Nova de Lisboa, Portugal and at University of Tübingen, Germany. His field of work is logic, e.g. formal arithmetic, provability logic, provability predicates, and paradoxes.

Blurb

In this book, Paulo Guilherme Santos studies diagonalization in formal mathematics from logical aspects to everyday mathematics. He starts with a study of the diagonalization lemma and its relation to the strong diagonalization lemma. After that, Yablo’s paradox is examined, and a self-referential interpretation is given. From that, a general structure of diagonalization with paradoxes is presented. Finally, the author studies a general theory of diagonalization with the help of examples from mathematics.

Contents 

• Diagonalization in Mathematics
• Diagonalization Lemma
• Fixed Point Theorems
• Paradoxes: Liar, Yablo’s Paradox, Curry’s Paradox

Target Groups

Researchers and students in the fields of mathematics and philosophy 

The Author

Paulo Guilherme Santos is currently a PhD student at FCT, Universidade Nova de Lisboa, Portugal and at University of Tübingen, Germany. His field of work is logic, e.g. formal arithmetic, provability logic, provability predicates, and paradoxes.