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Free set algebras satisfying systems of equations

Published online by Cambridge University Press:  12 March 2014

G. Aldo Antonelli*
Program in Logic and Philosophy of Science, University of California, Irvine 3151 Social Science Plaza Irvine, CA 92697-5100, USA, E-mail:


In this paper we introduce the notion of a set algebra satisfying a system E of equations. After defining a notion of freeness for such algebras, we show that, for any system E of equations, set algebras that are free in the class of structures satisfying E exist and are unique up to a bisimulation. Along the way, analogues of classical set-theoretic and algebraic properties are investigated.

Research Article
Copyright © Association for Symbolic Logic 1999

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[1]Aczel, P., Non-well-founded sets, Center for the Study of Language and Information, Stanford, CA, 1988.Google Scholar
[2]Antonelli, G.A., Non-well-founded sets via revision rules, Journal of Philosophical Logic, vol. 23 (1994), pp. 633–79, Mathematical Reviews 95k:03086.CrossRefGoogle Scholar
[3]Antonelli, G.A., Extensional quotients for type theory and the consistency problem for NF, this Journal, vol. 63 (1998), no. 1, pp. 247261.Google Scholar
[4]Barwise, J. and Moss, L., Vicious circles, Center for the Study of Language and Information, Stanford, CA, 1996.Google Scholar
[5]Cohn, P.M., Universal algebra, D. Reidel Publishing Co., Dordrecht and Boston, 1965, 1981.CrossRefGoogle Scholar
[6]Joyal, A. and Moerdijk, I., Algebraic set theory, London Mathematical Society Lecture Note Series, no. 220, Cambridge University Press, Cambridge, 1995.CrossRefGoogle Scholar
[7]Mislove, M., Moss, L., and Oles, F., Non-well-founded sets obtained from ideal fixed points, Information and Computation, vol. 93 (1991), no. 1, pp. 1654.CrossRefGoogle Scholar
[8]Robinson, D.J.S., A course in the theory of groups, Springer Verlag, Berlin and New York, 1982.CrossRefGoogle Scholar