Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Witnessing differences without redundancies


Authors: Franco Parlamento, Alberto Policriti and K. P. S. B. Rao
Journal: Proc. Amer. Math. Soc. 125 (1997), 587-594
MSC (1991): Primary 03E05; Secondary 03E25
DOI: https://doi.org/10.1090/S0002-9939-97-03630-7
MathSciNet review: 1353394
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that $\: n-1 \:$ elements suffice to witness the differences of $\: n \:$ pairwise distinct sets, and provide sufficient conditions for an infinite family of pairwise distinct sets to have a minimal collection of elements witnessing the differences between any two of its members.


References [Enhancements On Off] (What's this?)

  • [Bol86] B. Bollobás, Combinatorics, Cambridge University Press, 1986. MR 88g:05001
  • [Bon72] J. A. Bondy, Induced subsets, Journal of Combinatorial Theory (B), vol. 12, pages 201-202, 1972. MR 47:8315
  • [CFO89] D. Cantone, A. Ferro, and E. G. Omodeo, Computable Set Theory. Vol. 1, Oxford University Press, 1989. Int. Series of Monographs on Computer Science, vol. 6. MR 91i:03002
  • [PP88] F. Parlamento and A. Policriti, The Logically Simplest Form of the Infinity Axiom, Proceedings of the American Mathematical Society, 103(1):274-276, May 1988. MR 89h:03086
  • [PP90] F. Parlamento and A. Policriti, Note on: The Logically Simplest Form of the Infinity Axiom, Proceedings of the American Mathematical Society, 108(1), 1990. MR 90d:03099
  • [PP92] F. Parlamento and A. Policriti, The Decision Problem for Restricted Universal Quantification in Set Theory and the Axiom of Foundation, Zeitschrift für Mathematische Logik und Grundlangen der Mathematik, 38(2):143-156, 1992. MR 95c:03029

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 03E05, 03E25

Retrieve articles in all journals with MSC (1991): 03E05, 03E25


Additional Information

Franco Parlamento
Affiliation: Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 204, 33100 Udine–Italy
Email: parlamen@dimi.uniud.it

Alberto Policriti
Email: policrit@dimi.uniud.it

K. P. S. B. Rao
Affiliation: Indian Statistical Institute Bangalore, 8th mile Mysore Road, R.V. College Post, Bangalore 560 059
Email: kpsbrao@isibang.ernet.in

DOI: https://doi.org/10.1090/S0002-9939-97-03630-7
Received by editor(s): February 7, 1994
Received by editor(s) in revised form: August 28, 1995
Additional Notes: This work has been supported by funds MURST 40% and 60% of Italy.
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society