Diagonalization in Formal Mathematics
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Beschreibung
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
The AuthorPaulo Guilherme Santos is currently a PhD student at FCT, Universidade Nova de Lisboa, Portugal and atUniversity of Tübingen, Germany. His field of work is logic, e.g. formal arithmetic, provability logic, provability predicates, and paradoxes.
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.
Publication in the field of natural sciences
Autor*in
Paulo Guilherme Santos
Themen in »Diagonalization in Formal Mathematics«
Diagonalization Self-reference Paradoxes Fixed points Yablo’s paradox Smullyan’s theorem Curry’s paradox Russell’s paradox Diagonalization lemma Lawvere’s diagonal argument Knaster–Tarski theorem Banach theorem