Pacific Journal of Mathematics

Constructive versions of Tarski's fixed point theorems.

Patrick Cousot and Radhia Cousot

Article information

Source
Pacific J. Math., Volume 82, Number 1 (1979), 43-57.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102785059

Mathematical Reviews number (MathSciNet)
MR549831

Zentralblatt MATH identifier
0413.06004

Subjects
Primary: 06A23
Secondary: 03D20: Recursive functions and relations, subrecursive hierarchies

Citation

Cousot, Patrick; Cousot, Radhia. Constructive versions of Tarski's fixed point theorems. Pacific J. Math. 82 (1979), no. 1, 43--57. https://projecteuclid.org/euclid.pjm/1102785059


Export citation

References

  • [1] S. Abian and A. B. Brown, A theorem on partially ordered sets withapplications to fixed point theorems, Canad. J. Math., 13 (1961), 78-82.
  • [2] H. Amann, Fixed point equations and non-linear eigenvalue problems in ordered Banach spaces, SIAM Review 18, 4 (October 1976),620-709.
  • [3] G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloquium Publications 25, 3rd ed., Providence, Rhode Island, (1976).
  • [4] A. Church, The calculi of lambda-conversion, Annals of Math. Studies, 6 (1951), Princeton University Press, Princeton, N.J.
  • [5] P. Cousot and R. Cousot, Abstract interpretation:a unified lattice model for static analysis of programs by construction or approximation of fixpoints, Conf. Rec.of the Fourth ACM Symp. on Principles of Programming Languages, Los Angeles, Calif. (Jan. 1977), 238-252.
  • [6] R. DeMarr, Common fixed points for isotone mappings, Colloquium Math., 13 (1964), 45-48.
  • [7] V. Devide, On monotonous mappings of complete lattices, Fundamenta Mathematicae, LIII (1964), 147-154.
  • [8] P. Hitchcock and D. Park, Induction rules and proofs of termination,Proc. of a Symp. on Automata, Languages and Programming, North-Holland Pub.Co.,Amsterdam, (1973), 225-251.
  • [9] H. Hft and M. Hft, Some fixed point theorems for partially ordered sets, Canad. J. Math., 5 (1976), 992-997.
  • [10] S. C. Kleene, Introduction to metamathematics, North-Holland Pub.Co.,Amsterdam, (1952).
  • [11] I. I. Kolodner, On completeness of partially ordered sets and fixpoints theorems for isotone mappings, Amer. Math. Monthly, 75 (1968), 48-49.
  • [12] Y. Ladegaillerie, Prefermeture sur un ensemble ordonne, RAIRO, 1 (Avril 1973), 35-43.
  • [13] Z. Manna and A. Shamir, The convergence of functions to fixed points of recursive definitions, Theoretical Computer Science, 6 (1978), 109-141.
  • [14] G. Markowsky, Chain-complete posets and directed sets with applications, Algebra Univ., 6 (1976), 53-58, Birkhaser Verlag, Basel.
  • [15] A. Pasini, Some fixed point theorems of the mappings of partially ordered sets, Rend. Sem. Mat. Univ. Padova, 51 (1974), 167-177.
  • [16] A. Pelczar, On the invariant points of a transformation,Ann. Polon. Math., 11 (1961), 199-202.
  • [17] A. Pelczar, Remarks on commutings mappings in partially ordered spaces, Zeszyty Nauk. Univ. Jagiello., Prace Mat. Zeszyt, 15 (1971), 131-133.
  • [18] R. E. Smithson, Fixed points in partially ordered sets, Pacific J. Math., 1 (1973), 363-367.
  • [19] A. Tarski, A lattice theoretical fixpoint theorem and its applications, Pacific J. Math., 5 (1955), 285-310.
  • [20] L. E. Ward Jr., Completeness in semi-lattices, Canad. J. Math., 9 (1957), 578-582.
  • [21] M. Ward, The closure operators of a lattice, Annals Math., 43 (1942), 191-196.
  • [22] E. S. Wolk, Dedekind completeness and a fixed point theorem, Canad. J. Math., 9 (1957), 400-405.
  • [23] J. S. W. Wong, Common fixed points of commuting monotone mapping, Canad. J. Math., 19 (1967), 617-620.