Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

 

 

Fixed point algebras


Author: C. Smoryński
Journal: Bull. Amer. Math. Soc. 6 (1982), 317-356
MSC (1980): Primary 03-02, 03G05; Secondary 03B45, 03F30
MathSciNet review: 648523
Full-text PDF

References | Similar Articles | Additional Information

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

  • 1. S. N. Artemov, Arithmetically complete modal theories, Semiotics and information science, No. 14 (Russian), Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1980, pp. 115–133 (Russian). MR 585332
  • 2. Fabio Bellissima, On the modal logic corresponding to diagonalizable algebra theory, Boll. Un. Mat. Ital. B (5) 15 (1978), no. 3, 915–930 (English, with Italian summary). MR 524111
  • 3. Claudio Bernardi, The fixed-point theorem for diagonalizable algebras, Studia Logica 34 (1975), no. 3, 239–251. The algebraization of the theories which express Theor, III. MR 0460110
  • 4. Claudio Bernardi, On the equational class of diagonalizable algebras, Studia Logica 34 (1975), no. 4, 321–331. The algebraization of the theories which express Theor, VI. MR 0460113
  • 5. Claudio Bernardi, The uniqueness of the fixed-point in every diagonalizable algebra, Studia Logica 35 (1976), no. 4, 335–343. The algebraization of the theories which express Theor, VIII. MR 0460115
  • 6. S. Feferman, Arithmetization of metamathematics in a general setting, Fund. Math. 49 (1960/1961), 35–92. MR 0147397
  • 7. Cyril F. Gardiner, A first course in group theory, Springer-Verlag, New York-Berlin, 1980. Universitext. MR 600652
  • 8. G. Gargov, A note on the provability logics of certain extensions of Heyting's arithmetic (to appear).
  • 9. Kurt Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatsh. Math. Phys. 38 (1931), no. 1, 173–198 (German). MR 1549910, 10.1007/BF01700692
  • 10. D. Guaspari, Partially conservative extensions of arithmetic, Trans. Amer. Math. Soc. 254 (1979), 47–68. MR 539907, 10.1090/S0002-9947-1979-0539907-7
  • 11. D. Guaspari and R. M. Solovay, Rosser sentences, Ann. Math. Logic 16 (1979), no. 1, 81–99. MR 530432, 10.1016/0003-4843(79)90017-2
  • 12. Petr Hájek, On interpretability in set theories, Comment. Math. Univ. Carolinae 12 (1971), 73–79. MR 0311470
  • 13. Petr Hájek, On interpretability in set theories. II, Comment. Math. Univ. Carolinae 13 (1972), 445–455. MR 0323566
  • 14. Marie Hájková, The lattice of bi-numerations of arithmetic. I, Comment. Math. Univ. Carolinae 12 (1971), 81–104. MR 0284336
  • 15. Paul R. Halmos, Algebraic logic. I. Monadic Boolean algebras, Compositio Math. 12 (1956), 217–249. MR 0078304
  • 16. C. F. Kent, “Disorder” in lattices of binumerations, Comment. Math. Univ. Carolinae 15 (1974), 221–244. MR 0351770
  • 17. M. H. Löb, Solution of a problem of Leon Henkin, J. Symb. Logic 20 (1955), 115–118. MR 0070596
  • 18. A. Macintyre and H. Simmons, Gödel’s diagonalization technique and related properties of theories, Colloq. Math. 28 (1973), 165–180. MR 0332465
  • 19. Roberto Magari, Problemi aperti sulle algebre diagonali, Rend. Sem. Mat. Fis. Milano 44 (1974), 75–90 (1975). MR 0398825
  • 20. Roberto Magari, Metodi algebrici in teoria della dimostrazione, Boll. Un. Mat. Ital. (4) 12 (1975), no. 3, 252–261 (Italian). MR 0419184
  • 21. Roberto Magari, The diagonalizable algebras, Boll. Un. Mat. Ital. (4) 12 (1975), no. 3, suppl., 117–125 (English, with Italian summary). The algebraization of the theories which express Theor, II; Collection in memory of Enrico Bompiani. MR 0460109
  • 22. Roberto Magari, Representation and duality theory for diagonalizable algebras, Studia Logica 34 (1975), no. 4, 305–313. The algebraization of the theories which express Theor, IV. MR 0460111
  • 23. Roberto Magari, On the autological character of diagonalizable algebras, Studia Logica 35 (1976), no. 4, 327–333. The algebraization of the theories which express Theor, VII. MR 0460114
  • 24. Roberto Magari, Modal diagonalizable algebras, Boll. Un. Mat. Ital. B (5) 15 (1978), no. 1, 303–320 (English, with Italian summary). MR 0505479
  • 25. Larry Manevitz and Jonathan Stavi, Δ⁰₂ operators and alternating sentences in arithmetic, J. Symbolic Logic 45 (1980), no. 1, 144–154. MR 560232, 10.2307/2273361
  • 26. Massimo Mirolli, On the axiomatization of finite frames of the modal system 𝐺𝐿, Boll. Un. Mat. Ital. B (5) 17 (1980), no. 3, 1075–1085 (English, with Italian summary). MR 770833
  • 27. Franco Montagna, For every 𝑛, the 𝑛-freely generated algebra is not functionally free in the equational class of diagonalizable algebras, Studia Logica 34 (1975), no. 4, 315–319. The algebraization of the theories which express Theor, V. MR 0460112
  • 28. Franco Montagna, On the algebraization of a Feferman’s predicate, Studia Logica 37 (1978), no. 3, 221–236. MR 515168, 10.1007/BF02124724
  • 29. Franco Montagna, On the diagonalizable algebra of Peano arithmetic, Boll. Un. Mat. Ital. B (5) 16 (1979), no. 3, 795–812 (English, with Italian summary). MR 553798
  • 30. Franco Montagna, Interpretations of the first-order theory of diagonalizable algebras in Peano arithmetic, Studia Logica 39 (1980), no. 4, 347–354. MR 611997, 10.1007/BF00713544
  • 31. Franco Montagna, The undecidability of the first-order theory of diagonalizable algebras, Studia Logica 39 (1980), no. 4, 355–359. MR 611998, 10.1007/BF00713545
  • 32. Steven Orey, Relative interpretations, Z. Math. Logik Grundlagen Math. 7 (1961), 146–153. MR 0146082
  • 33. Stanislav Palúch, The lattices of numerations of theories containing Peano’s arithmetic, Comment. Math. Univ. Carolinae 14 (1973), 339–359. MR 0360253
  • 34. J. B. Rosser, Extensions of some theorems of Gödel and Church, J. Symbolic Logic 1 (1936), 87-91.
  • 35. Giovanni Sambin, Un’estensione del teorema di Löb, Rend. Sem. Mat. Univ. Padova 52 (1974), 193–199 (1975) (Italian, with English summary). MR 0384501
  • 36. Giovanni Sambin, An effective fixed-point theorem in intuitionistic diagonalizable algebras, Studia Logica 35 (1976), no. 4, 345–361. The algebraization of the theories which express Theor, IX. MR 0460116
  • 37. Giovanni Sambin, Fixed points through the finite model property, Studia Logica 37 (1978), no. 3, 287–289. MR 515173, 10.1007/BF02124729
  • 38. G. Sambin, Topology and categorical duality in the study of semantics for model logics (to appear).
  • 39. Krister Segerberg, An essay in classical modal logic. Vols. 1, 2, 3, Filosofiska Föreningen och Filosofiska Institutionen vid Uppsala Universitet, Uppsala, 1971. Filosofiska Studier, No. 13. MR 0339999
  • 40. H. Simmons, Topological aspects of suitable theories, Proc. Edinburgh Math. Soc. (2) 19 (1974/75), no. 4, 383–391. MR 0387047
  • 41. Handbook of mathematical logic, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Edited by Jon Barwise; With the cooperation of H. J. Keisler, K. Kunen, Y. N. Moschovakis and A. S. Troelstra; Studies in Logic and the Foundations of Mathematics, Vol. 90. MR 0457132
  • 42. C. Smoryński, Beth’s theorem and self-referential sentences, Logic Colloquium ’77 (Proc. Conf., Wrocław, 1977) Stud. Logic Foundations Math., vol. 96, North-Holland, Amsterdam-New York, 1978, pp. 253–261. MR 519820
  • 43. Craig Smoryński, Calculating self-referential statements. I. Explicit calculations, Studia Logica 38 (1979), no. 1, 17–36. MR 542417, 10.1007/BF00493670
  • 44. C. Smoryński, Calculating self-referential statements, Fund. Math. 109 (1980), no. 3, 189–210. MR 597066
  • 45. C. Smoryński, Calculating self-referential statements: Guaspari sentences of the first kind, J. Symbolic Logic 46 (1981), no. 2, 329–344. MR 613286, 10.2307/2273625
  • 46. C. Smoryński, Fifty years of self-reference in arithmetic, Notre Dame J. Formal Logic 22 (1981), no. 4, 357–374. MR 622365
  • 47. C. Smoryński, A ubiquitous fixed point calculation, "Interpretability"; Proceedings of the First Joint Conference on the Foundations of Mathematics Organised by the Białystok Branch of the Warsaw University and Humboldt University (Berlin) (L. Szczerba and K. Prażmowski, eds.), Doktorce 1980, Filia Uniwersytetu Warszawskiego w Białymstoku (to appear).
  • 48. C. Smoryński, Commutativity and self-reference, Notre Dame J. Formal Logic 23 (1982), no. 4, 443–452. MR 669150
  • 49. Craig Smoryński, The finite inseparability of the first-order theory of diagonalisable algebras, Studia Logica 41 (1982), no. 4, 347–349 (1983). MR 764759, 10.1007/BF00403334
  • 50. Robert M. Solovay, Provability interpretations of modal logic, Israel J. Math. 25 (1976), no. 3-4, 287–304. MR 0457153
  • 51. R. M. Solovay, On interpretability in set theories (to appear).
  • 52. Stefano Stefani, On the representation of hemimorphisms between Boolean algebras, Boll. Un. Mat. Ital. (5) 13A (1976), no. 1, 206–211 (English, with Italian summary). MR 0417010
  • 53. M. H. Stone, The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40 (1936), no. 1, 37–111. MR 1501865, 10.1090/S0002-9947-1936-1501865-8
  • 54. Vítězslav Švejdar, A sentence that is difficult to interpret, Comment. Math. Univ. Carolin. 22 (1981), no. 4, 661–666. MR 647015
  • 55. Aldo Ursini, Intuitionistic diagonalizable algebras, Algebra Universalis 9 (1979), no. 2, 229–237. MR 523937, 10.1007/BF02488034
  • 56. Aldo Ursini, A modal calculus analogous to 𝐾4𝑊, based on intuitionistic propositional logic. I, Studia Logica 38 (1979), no. 3, 297–311. MR 560490, 10.1007/BF00405387
  • 57. Albert Visser, An inside view of 𝐸𝑋𝑃; or, The closed fragment of the provability logic of 𝐼Λ₀+Ω₁ with a propositional constant for 𝐸𝑋𝑃, J. Symbolic Logic 57 (1992), no. 1, 131–165. MR 1150930, 10.2307/2275181

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1980): 03-02, 03G05, 03B45, 03F30

Retrieve articles in all journals with MSC (1980): 03-02, 03G05, 03B45, 03F30


Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1982-15002-9