Incompleteness for Higher-Order Arithmetic An Example Based on Harrington’s Principle
The book examines the following foundation question: are all theorems in classic mathematics which are expressible in second order arithmetic provable in second order arithmetic? In this book, the author gives a counterexample for this question and isolates this counterexample from Martin-Harrington...
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| Autor Corporativo: | |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Singapore :
Springer Singapore
2019.
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| Edición: | 1st ed |
| Colección: | Springer eBooks.
SpringerBriefs in Mathematics. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b39903047*spi |
| Sumario: | The book examines the following foundation question: are all theorems in classic mathematics which are expressible in second order arithmetic provable in second order arithmetic? In this book, the author gives a counterexample for this question and isolates this counterexample from Martin-Harrington theorem in set theory. It shows that the statement zHarrington’s principle implies zero sharpy is not provable in second order arithmetic. The book also examines what is the minimal system in higher order arithmetic to show that Harrington’s principle implies zero sharp and the large cardinal strength of Harrington’s principle and its strengthening over second and third order arithmetic. . |
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| Descripción Física: | XIV, 122 p. : 1 il |
| Formato: | Forma de acceso: World Wide Web. |
| ISBN: | 9789811399497 |
