Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-24T02:54:49.110Z Has data issue: false hasContentIssue false

Maximal compatible extensions of partial orders

Published online by Cambridge University Press:  09 April 2009

Stephan Foldes
Affiliation:
Institute of Mathematics, Tampere University of Technology, PL 553, 33101 Tampere, Finnland, e-mail: [email protected]
Jenő Szigeti
Affiliation:
Institute of Mathematics, University of Miskolc, Miskolc 3515, Hungary, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a complete description of maximal compatible partial orders on the mono-unary algebra (A, f), where f: A → A is an arbitrary unary operation.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Bonnet, R. and Pouzet, M., ‘Linear extensions of ordered sets’, in: Ordered Sets (ed. Rival, I.), Proceedings of the Nato Advanced Study Institute Conference held in Banff, August 28–September 12, 1981 (D. Reidel Publishing Co., Dordrecht, 1982) pp. 125170.CrossRefGoogle Scholar
[2]Bosi, G. and Herden, G., ‘On a strong continuous analogue of the Szpilrajn theorem and its strengthening by Dushnik and Miller’, Order 22 (2005), 329342.CrossRefGoogle Scholar
[3]Downey, R. G., Hirschfeldt, D. R., Lempp, S. and Solomon, R., ‘Computability-theoretic and proof- theoretic aspects of partial and linear orderings’, Israel J. Math. 138 (2003), 271289.CrossRefGoogle Scholar
[4]Herden, G. and Pallack, A., ‘On the continuous analogue of the Szpilrajn theorem I’, Math. Social Sci. 43 (2002), 115134.CrossRefGoogle Scholar
[5]Körtesi, P., Radeleczki, S. and Szilágyi, Sz., ‘Congruences and isotone maps on partially ordered sets’, Math. Pannon. 16 (2005), 3955.Google Scholar
[6]Lahiri, S., ‘A simple proof of Suzumura's extension theorem for finite domains with applications’, J. Appl. Math. Decis. Sci. 6 (2002), 183190.CrossRefGoogle Scholar
[7]Novak, V. and Novotny, M., ‘Linear extensions of orderings’, Czechoslovak Math. J. 50 (2000), 853864.CrossRefGoogle Scholar
[8]Szigeti, J. and Nagy, B., ‘Linear extensions of partial orders preserving monotonicity’, Order 4 (1987), 3135.CrossRefGoogle Scholar
[9]Szpilrajn, E., ‘Sur l'extension de l'order partiel’, Fund. Math. 16 (1930), 386389.CrossRefGoogle Scholar