Skip to main content

On the recursion theorem in iterative operative spaces

  • J. Zashev (a1)

The recursion theorem in abstract partially ordered algebras, such as operative spaces and others, is the most fundamental result of algebraic recursion theory. The primary aim of the present paper is to prove this theorem for iterative operative spaces in full generality. As an intermediate result, a new and rather large class of models of the combinatory logic is obtained.

Hide All
[1]Barendregt H. P., The lambda calculus: Its syntax and semantics, Nort-Holland, Amsterdam, 1984.
[2]Ivanov L. L., A simpler first order mu-induction axiom for operative spaces, unpublished manuscript.
[3]Ivanov L. L., Iterative operative spaces, Ph.D. thesis, Sofia University, 1980. in Bulgarian.
[4]Ivanov L. L., Algebraic recursion theory, Ellis Horwood, Chichester, 1986.
[5]Kleene S. C., Introduction to metamathematics, Noordhof N. V., Groningen, 1952.
[6]Moschovakis Y. N., Abstract first order computability, Transactions of the American Mathematical Society, vol. 138 (1969), pp. 427504.
[7]Skordev D. G., Recursion theory on iterative combinatory spaces, Bulletin de l'Académie Polonaise des Sciences, vol. 24 (1976), pp. 2331.
[8]Skordev D. G., Some models of combinatory logic, Mathematical Notes, vol. 19 (1976), no. 1, pp. 8890.
[9]Skordev D. G., Combinatory spaces and recursiveness in them, BAN, Sofia, 1980, in Russian. English summary.
[10]Skordev D. G., Computability in Combinatory Spaces, 1992, Amsterdam.
[11]Zashev J., Diagonal fixed points in algebraic recursion theory, submitted.
[12]Zashev J., Recursion theory in partially ordered combinatory models, Ph.D. thesis, Sofia University, 1983, (In Bulgarian).
[13]Zashev J., Least fixed points in preassociative combinatory algebras, Mathematical logic (Petkov P., editor), Plenum Press, New York, 1990, pp. 389397.
[14]Zashev J., Categorial generalization of algebraic recursion theory, Journal of Pure and Applied Algebra, vol. 101 (1995), pp. 91128.
[15]Zashev J., First order axiomatizability of recursion theory in cartesian linear combinatory algebras, Annuaire de l'Université de Sofia “St. Kliment Okhridski”. Faculté de Mathématiques et Informatique, vol. 90 (1998), pp. 4150.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 3 *
Loading metrics...

Abstract views

Total abstract views: 50 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 15th December 2017. This data will be updated every 24 hours.