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,
$24.95$
Peter Aczel, Non-well-founded sets, CSLI Lecture Notes, vol. 14, Stanford University, Center for the Study of Language and Information, Stanford, CA, 1988. With a foreword by Jon Barwise [K. Jon Barwise]. MR 940014
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
Marco Forti and Furio Honsell, Set theory with free construction principles, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 10 (1983), no. 3, 493–522. MR 739920
Kenneth Kunen, Set theory, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam-New York, 1980. An introduction to independence proofs. MR 597342
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
Yiannis N. Moschovakis, Notes on set theory, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1994. MR 1260432, DOI 10.1007/978-1-4757-4153-7
[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
- [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
DOI:
https://doi.org/10.1090/S0273-0979-98-00735-6
Review copyright:
© Copyright 1998
American Mathematical Society