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Book Review

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Book Information

Author(s): Jon Barwise and Larry Moss
Title: Vicious circles: On the mathematics of non-wellfounded phenomena
Additional book information: CSLI Publications, Stanford, CA, 1996, iv + 390, $24.95, 1-57586-008-2

References:

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P. Aczel. Non-well-founded sets. Number 14 in CSLI Lecture Notes. Center for the Study of Languages and Information, Stanford, 1988. MR 89j:03039

[AJ94]
S. Abramsky and A. Jung. Domain theory. In S. Abramsky, D.M. Gabbay, and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, volume 3. Oxford Univ. Press, 1994. MR 97b:68121

[AM82]
M.A. Arbib and E.G. Manes. Parametrized data types do not need highly constrained parameters. Information and Control, 52(2):139-158, 1982. MR 84i:68014

[AM89]
P. Aczel and N. Mendler. A final coalgebra theorem. In D.H. Pitt, D.E. Ryeheard, P. Dybjer, A. M. Pitts, and A. Poigne, editors, Proceedings category theory and computer science, Lecture Notes in Computer Science, pages 357-365, 1989. MR 91f:18001

[Bar93]
M. Barr. Terminal coalgebras in well-founded set theory. Theoretical Computer Science, 114(2):299-315, June 1993. Some additions and corrections were published in TCS Vol. 124, 1994, pp. 189-192. MR 94m:18006a; MR 94m:18006b

[BM97]
J. Barwise and L.S. Moss. Modal correspondence for models. Journal of Philosophical Logic, 1997. To appear.

[BV96]
J.W. de Bakker and E. de Vink. Control Flow Semantics. Foundations of Computing Series. The MIT Press, 1996. MR 96h:68074

[BZ82]
J.W. de Bakker and J.I. Zucker. Processes and the denotational semantics of concurrency. Information and Control, 54(1/2):70-120, July/August 1982. MR 85e:68056

[Dev93]
K. Devlin. The Joy of Sets. Undergraduate Texts in Mathematics. Springer-Verlag, 1993. MR 94e:03001

[FH83]
M. Forti and F. Honsell. Set theory with free construction principles. Annali Scuola Normale Superiore di Pisa, X(3):493-522, 1983. MR 85f:03054

[Kun80]
K. Kunen. Set Theory, volume 102 of Studies in logic and the foundations of mathematics. North-Holland, 1980. MR 82f:03001

[MA86]
E.G. Manes and M.A. Arbib. Algebraic approaches to program semantics. Texts and Monographs in Computer Science. Springer-Verlag, 1986. MR 88d:68069

[MD97]
L.S. Moss and N. Danner. On the foundations of corecursion. Logic Journal of the IGPL, pages 231-257, 1997. CMP 97:08

[Mil80]
R. Milner. A Calculus of Communicating Systems, volume 92 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1980. MR 82g:68001

[ML71]
S. Mac Lane. Categories for the Working Mathematician, volume 5 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1971. MR 50:7275

[Mos94]
Y.N. Moschovakis. Notes on set theory. Undergraduate Texts in Mathematics. Springer-Verlag, 1994. MR 95a:04001

[Mos97]
L.S. Moss. Coalgebraic logic. Annals of Pure and Applied Logic, 1997. To appear.

[MS96]
L.S. Moss and J. Seligman. Situation theory. In J. van Benthem and A. ter Meulen, editors, Handbook of Logic and Language, chapter 4, pages 239-309. Kluwer Acad. Publishers, 1996.

[Par81]
D.M.R. Park. Concurrency and automata on infinite sequences. In P. Deussen, editor, Proceedings 5th GI conference, volume 104 of Lecture Notes in Computer Science, pages 15-32. Springer-Verlag, 1981.

[RT94]
J.J.M.M. Rutten and D. Turi. Initial algebra and final coalgebra semantics for concurrency. In J.W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Proceedings of the REX School/Symposium `A decade of concurrency', volume 803 of Lecture Notes in Computer Science, pages 530-582. Springer-Verlag, 1994. FTP-available at ftp.cwi.nl as pub/CWIreports/AP/CS-R9409.ps.Z. MR 96d:68141

[SP82]
M.B. Smyth and G.D. Plotkin. The category-theoretic solution of recursive domain equations. SIAM Journal of Computation, 11(4):761-783, November 1982. MR 84d:68052

Additional Information:

Reviewer(s):
J. J. M. M. Rutten
Affiliation: Centrum voor Wiskunde en Informatica (CWI)
Email: janr@cwi.nl

Review Information:
Journal: Bull. Amer. Math. Soc. 35 (1998), 69-75.

MSC (1991): Primary 03-XX, 04-XX, 68-XX, 90-XX, 94-XX
DOI: 10.1090/S0273-0979-98-00735-6
PII: S 0273-0979(98)00735-6
Copyright of article: Copyright 1998, American Mathematical Society

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