Book Review

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Book Information:

Authors: 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 pp., ISBN 1-57586-008-2, $24.95

**[Acz88]**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**

Review Information:

Reviewer: J. J. M. M. Rutten

Affiliation: Centrum voor Wiskunde en Informatica (CWI)

Email: janr@cwi.nl

Journal: Bull. Amer. Math. Soc.

**35**(1998), 69-75

MSC (1991): Primary 03-XX, 04-XX, 68-XX, 90-XX, 94-XX

DOI: https://doi.org/10.1090/S0273-0979-98-00735-6

Review copyright: © Copyright 1998 American Mathematical Society