The Mirimanov paradox (the paradox of the class of all funded classes ) is a paradox in set theory , which is a generalization of the Burali-Forti paradox [1] . It is named after the mathematician Dmitry Mirimanov .
Content
Wording
Class called unfunded (funded) if there is (not) such an infinite sequence of classes , what:
- .
The term comes from English. well-founded .
The paradox lies in the fact that both the assumption that the class is well-founded of all funded classes and the assumption that it is not funded lead to a contradiction similar to the contradiction in the Russell paradox .
This paradox, like the Russell paradox, can be resolved in the semantics of self-belonging [2] .
Notes
- ↑ Cantini, 2012 .
- ↑ Chechulin, 2010 .
Literature
- Shen Yuting. Paradox of the Class of All Grounded Classes // J. Symb. Log .. - 1953. - T. 18 , No. 2 . - S. 114 . (Abstract in Russian Mathematics, Mathematics, 1954, No. 5027, referent A. Kuznetsov)
- Forster, Thomas and Libert, Thierry. An Order-Theoretic Account of Some Set-Theoretic Paradoxes // Notre Dame journal of formal logic. - 2011. - T. 52 , No. 1 . - S. 1-19 .
- Chechulin V.L. Self-belonging set theory (foundations and some applications). - Perm: Perm State University, 2010. - 100 p. - (Monograph). - ISBN 978-5-7944-1468-4 .
- Mirimanoff, D. , “Les antinomies de Russell et de Burali-Forti et le problème fondamentale de la théorie des ensembles”, L'Enseignement Mathématique, 19: 37–52, 1917.
Links
- Cantini, Andrea. Paradoxes and Contemporary Logic . - 2012.