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Non-well-founded sets modeled as ideal fixed points. (English) Zbl 0723.03031

See the review of the preliminary short version in Logic in computer science, Proc. 4th Annual Symp., Pacific Grove/CA (USA) 1989, 263-272 (1989; Zbl 0717.03023).

MSC:

03E65 Other set-theoretic hypotheses and axioms
68Q65 Abstract data types; algebraic specification
06B35 Continuous lattices and posets, applications

Citations:

Zbl 0717.03023
Full Text: DOI

References:

[1] Abramsky, S.; Abramsky, S.
[2] Aczel, P., Non-Well-Founded Sets, (CSLI Lecture Notes, No. 14 (1988), Stanford University: Stanford University Stanford, CA) · Zbl 0668.04001
[3] Goguen, J.; Thatcher, J. W.; Wagner, E. G.; Wright, J. B., Rational algebraic theories and fixed-point solutions, (Proceedings, 17th IEEE Symposium on Foundations of Computing. Proceedings, 17th IEEE Symposium on Foundations of Computing, Oct. 1976 (1976)), 147-158, ADJ
[4] Goguen, J. A.; Thatcher, J. W.; Wagner, E. G.; Wright, J. B., Initial algebra semantics and continuous algebras, (J. Assoc. Comput. Mach., 24 (1977)), 68, ADJ · Zbl 0359.68018
[5] Barwise, J.; Etchemendy, J., (The Liar: An Essay in Truth and Circularity (1988), Oxford Univ. Press: Oxford Univ. Press Oxford)
[6] Barwise, J., Three views of common knowledge, (Vardi, M., Theoretical Aspects of Reasoning About Knowledge II (1988)), 365-380 · Zbl 0704.03008
[7] Boffa, M.; Boffa, M.
[8] Gierz, G.; Hofmann, K. H.; Keimel, K.; Lawson, J. D.; Mislove, M. W.; Scott, D. S., (A Compendium of Continuous Lattices (1980), Springer-Verlag: Springer-Verlag Berlin/New York/Heidelberg) · Zbl 0452.06001
[9] Fernando, T., On recursion over non-well-founded sets, (Proceedings, Fourth Symposium on Logic in Computer Science. Proceedings, Fourth Symposium on Logic in Computer Science, IEEE, 1989 (1989)), 273-282 · Zbl 0724.03032
[10] Hennessy, M., (Algebraic Theory of Processes (1988), MIT Press: MIT Press Cambridge, MA) · Zbl 0744.68047
[11] Milner, R., Calculi for synchrony and asynchrony, Theoret. Comput. Sci., 25, 267 (1983) · Zbl 0512.68026
[12] Mislove, M. W.; Moss, L. S.; Oles, F. J., Non-well-founded sets obtained from ideal fixed points, (Proceedings, Fourth Symposium on Logic in Computer Science. Proceedings, Fourth Symposium on Logic in Computer Science, IEEE, 1989 (1989)), 263-272 · Zbl 0717.03023
[13] Mislove, M. W.; Moss, L. S.; Oles, F. J., Partial sets, (Cooper, R.; Mukai, K.; Perry, J., Situation Theory and its Applications. Situation Theory and its Applications, CSLI Lecture Notes, No. 22 (1989), Stanford University: Stanford University Stanford, CA)
[14] Möller, B., On the algebraic specification of infinite objects—ordered and continuous models of algebraic types, Acta Informat., 22, 537-538 (1985) · Zbl 0563.68030
[15] Plotkin, G. D., A powerdomain construction, SIAM J. Comput., 5, 452 (1976) · Zbl 0355.68015
[16] Smyth, M. B.; Plotkin, G. D., The category-theoretic solution of recursive domain equations, SIAM J. Comput., 11, 761 (1982) · Zbl 0493.68022
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