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Interpretability in Robinson's Q

Published online by Cambridge University Press:  05 September 2014

Fernando Ferreira  and
Gilda Ferreira
Fernando Ferreira
Affiliation:
Universidade de Lisboa, Faculdade de Ci'encias, Departamento de Matemática, Campo Grande, ED. C6 1749-016 Lisboa, Portugal E-mail: fjferreira@fc.ul.pt Universidade Lusófona de Humanidades e Tecnologias, Departamento de Matemática, AV. Do Campo Grande 376, 1749-024 Lisboa, Portugal
Gilda Ferreira
Affiliation:
Universidade de Lisboa, Faculdade de Ciências, Departamento de Matemática, Campo Grande, ED. C6, 1749-016 Lisboa, Portugal E-mail: gildafer@cii.fc.ul.pt
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Abstract

Edward Nelson published in 1986 a book defending an extreme formalist view of mathematics according to which there is an impassable barrier in the totality of exponentiation. On the positive side, Nelson embarks on a program of investigating how much mathematics can be interpreted in Raphael Robinson's theory of arithmetic . In the shadow of this program, some very nice logical investigations and results were produced by a number of people, not only regarding what can be interpreted in but also what cannot be so interpreted. We explain some of these results and rely on them to discuss Nelson's position.

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Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 19 , Issue 3 , September 2013 , pp. 289 - 317
Copyright
Copyright © Association for Symbolic Logic 2013

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