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On a Problem of Formal LogicProceedings of The London Mathematical Society
- Publisher
- Springer Journals
- Copyright
- Copyright © 1985 by Verlag W. Kohlhammer
- Subject
- Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/BF02007556
- Publisher site
- See Article on Publisher Site
Abstract
In this paper we exposit some as yet unpublished results of Harvey Friedman. These results provide the most dramatic examples so far known of mathematically meaningful theorems of finite combinatorics which are unprovable in certain logical systems. The relevant logical systems,ATR 0 and Π 1 1 —CA 0, are well known as relatively strong fragments of second order arithmetic. The unprovable combinatorial theorems are concerned with embeddability properties of finite trees. Friedman's method is based in part of the existence of a close relationship between finite trees on the one hand, and systems of ordinal notations which occur in Gentzen-style proof theory on the other.
Journal
Archive for Mathematical Logic – Springer Journals
Published: Jul 13, 2005