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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
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, $24.95$

References [Enhancements On Off] (What's this?)

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  • Samson Abramsky and Achim Jung, Domain theory, Handbook of logic in computer science, Vol. 3, Handb. Log. Comput. Sci., vol. 3, Oxford Univ. Press, New York, 1994, pp. 1–168. MR 1365749
  • Michael A. Arbib and Ernest G. Manes, Parametrized data types do not need highly constrained parameters, Inform. and Control 52 (1982), no. 2, 139–158. MR 701590, DOI 10.1016/S0019-9958(82)80026-0
  • Peter Aczel and Nax Mendler, A final coalgebra theorem, Category theory and computer science (Manchester, 1989) Lecture Notes in Comput. Sci., vol. 389, Springer, Berlin, 1989, pp. 357–365. MR 1031572, DOI 10.1007/BFb0018361
  • Michael Barr, Terminal coalgebras in well-founded set theory, Theoret. Comput. Sci. 114 (1993), no. 2, 299–315. MR 1228862, DOI 10.1016/0304-3975(93)90076-6
  • [BM97]
    J. Barwise and L.S. Moss. Modal correspondence for models. Journal of Philosophical Logic, 1997. To appear.
  • Nathan Linial, Yishay Mansour, and Noam Nisan, Constant depth circuits, Fourier transform, and learnability, J. Assoc. Comput. Mach. 40 (1993), no. 3, 607–620. MR 1370363, DOI 10.1145/174130.174138
  • J. W. de Bakker and J. I. Zucker, Processes and the denotational semantics of concurrency, Inform. and Control 54 (1982), no. 1-2, 70–120. MR 713308, DOI 10.1016/S0019-9958(82)91250-5
  • Keith Devlin, The joy of sets, 2nd ed., Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1993. Fundamentals of contemporary set theory. MR 1237397, DOI 10.1007/978-1-4612-0903-4
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  • Ernest G. Manes and Michael A. Arbib, Algebraic approaches to program semantics, Texts and Monographs in Computer Science, Springer-Verlag, New York, 1986. AKM Series in Theoretical Computer Science. MR 860560, DOI 10.1007/978-1-4612-4962-7
  • [MD97]
    L.S. Moss and N. Danner. On the foundations of corecursion. Logic Journal of the IGPL, pages 231-257, 1997. CMP 97:08
  • Robin Milner, A calculus of communicating systems, Lecture Notes in Computer Science, vol. 92, Springer-Verlag, Berlin-New York, 1980. MR 590046
  • Saunders MacLane, Categories for the working mathematician, Graduate Texts in Mathematics, Vol. 5, Springer-Verlag, New York-Berlin, 1971. MR 0354798
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  • [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.
  • Jan Rutten and Daniele Turi, Initial algebra and final coalgebra semantics for concurrency, A decade of concurrency (Noordwijkerhout, 1993) Lecture Notes in Comput. Sci., vol. 803, Springer, Berlin, 1994, pp. 530–582. MR 1292686, DOI 10.1007/3-540-58043-3_{2}8
  • M. B. Smyth and G. D. Plotkin, The category-theoretic solution of recursive domain equations, SIAM J. Comput. 11 (1982), no. 4, 761–783. MR 677666, DOI 10.1137/0211062

  • 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
    DOI: https://doi.org/10.1090/S0273-0979-98-00735-6
    Review copyright: © Copyright 1998 American Mathematical Society