Algorithmic properties of finitely generated structures

  • Wiktor Dańko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 148)


We consider abstract structures and relations definable in those structures by formulas of Algorithmic Logic [1,3,14]. We notice that in the case where a structure is finitely generated every relation defined by an algorithmic formula can be defined by an algorithmic formula without classical quantifiers. Using the above fact we prove analogons of Łoś-Tarski Theorem for Algorithmic Logic and for Lω1ω.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    L.Banachowski, Investigations of properties of programs by means of the extended algorithmic logic, Fundamenta Informaticae I, 1977Google Scholar
  2. [2]
    W.Dańko, Programs with tables and procedures on the ground of algorithmic logic, doctoral dissertation, University of Warsaw, 1976Google Scholar
  3. [3]
    W.Dańko, Algorithmic logic with tables and classical quantifiers Zeszyty naukowe Filii UW w Białymstoku, (in print)Google Scholar
  4. [4]
    E.Engeler, Algorithmic properties of structures, Math. Sys. Theory I, 1967Google Scholar
  5. [5]
    M.Grabowski, The set of all tautologies of the zero order algorithmic logic is decidable, Bull.Acad.Polon.Sci. Sèr.Math.Astr.Phys., 20, 1972Google Scholar
  6. [6]
    H. Friedman, Algorithmic procedures, generalized Turing algorithms and elementary recursion theory, Logic Colloquium '69 North-Holland Publ. Co., Amsterdam 1971Google Scholar
  7. [7]
    D.Harel, A.Meyer, V.Pratt, Computability and completeness in logic of programs, MIT Cambridge Mess. May 1977Google Scholar
  8. [8]
    C.Hoare, An axiomatic basis of computer programming, Com. ACM 12, 1969Google Scholar
  9. [9]
    A.Kreczmar, Programmability in fields, Fundamenta Informaticae I 1977Google Scholar
  10. [10]
    D.Luckham, D.Park, M.Paterson, On formalized computer programs, ICSS 4, 1970Google Scholar
  11. [11]
    E.G.Lopez-Escobar, The interpolation theorem for denumerable long formulas, Fund.Math. 57, 1968Google Scholar
  12. [12]
    H.J. Keisler, Model theory for infinitary logic, North-Holland Publ. Co., Amsterdam 1972Google Scholar
  13. [13]
    G. Mirkowska, Algorithmic logic and its applications in program theory, Fund. Inf. I, 1977Google Scholar
  14. [14]
    G.Mirkowska, On formalized system of algorithmic logic, Bull. Acad.Polon.Sci.Sèr.Math.Astr.Phys. 19, 1971Google Scholar
  15. [15]
    H. Rasiowa, R. Sikorski, Mathematics of metamathematics, PWN, Warszawa, 1963Google Scholar
  16. [16]
    H.Rasiowa, On logical structure of programs, Bull.Acad.Polon.Sci.Sèr.Math.Astr.Phys. 20, 1972Google Scholar
  17. [17]
    A.Salwicki, On algorithmic theory of dictionaries, Fund. Inf. (in print)Google Scholar
  18. [18]
    A.Salwicki, Programmability and recursiveness, Dissertationes Mathematicae, (in print)Google Scholar
  19. [19]
    A.Salwicki, Formalized algorithmic languages, Bull.Acad.Polon. Sci.Sèr. Math.Astr.Phys. 18, 1970Google Scholar
  20. [20]
    J.C. Shepherdson, Computation over abstract structures, Logic Colloquium '73, North-Holland, Amsterdam 1973Google Scholar
  21. [21]
    J.Shoenfield, Mathematical logic, Addison-Wesley Publ. Co., 1967Google Scholar
  22. [22]
    J.Tiuryn, Logic of effective definitions, Fundamenta Informatice, (to appear) and R.W.T.H. Aachen Report 55, 1979Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Wiktor Dańko
    • 1
  1. 1.Institute of MathematicsUniversity of Warsaw, Białystok DivisionBiałystokPoland

Personalised recommendations