Skip to main content
SpringerLink
Log in

On the algebraization of a Feferman's predicate

The algebraization of theories which express Theor; X

  • Published:
Studia Logica Aims and scope Submit manuscript

Summary

This paper is devoted to the algebraization of an arithmetical predicate introduced by S. Feferman. To this purpose we investigate the equational class of Boolean algebras enriched with an operation ϱ, which translates such predicate, and an operation τ, which translates the usual predicate Theor. We deduce from the identities of this equational class some properties of ϱ and some ties between ϱ and τ; among these properties, let us point out a fixed-point theorem for a sufficiently large class of ϱ-τ polynomials. The last part of this paper concerns the duality theory for ϱ-τ algebras.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. Bernardi,The fixed-point theorem for diagonalizable algebras (the algebrai, zation of the theories which express Theor; III),Studia Logica, Vol. 34. No. 3 pp. 239–253.

  2. C. Bernardi,The uniqueness of the fixed-point in every diagonalizable algebra (the algebraization of the theories which express Theor; VIII),Studia Logica, Vol. 35, No. 4, pp. 335–345.

  3. S. Feferman,The Arithmetization of metamathematics in a general setting,Fundamenta Mathematicae, 1960.

  4. G. Gratzer,Universal Algebra, Van Nostrand, Princeton, 1968.

    Google Scholar 

  5. P. R. Halmos,Algebraic Logic, I. Monadic Boolean algebras,Çompositio Mathematica, Vol. 12 (1955), pp. 217–249 (reprinted in Algebraic logic, Chelsea Publishing Company, New York (1962)).

    Google Scholar 

  6. M. Löb,Solution of a problem of Leon Henkin,The Journal of Symbolic Logic, Vol. 20 (1955), pp. 115–118.

    Google Scholar 

  7. R. Magari,Problemi aperti sulle algebre diagonali, to appear inRendiconti del Seminario Matematico e Fisico di Milano.

  8. R. Magari,The diagonalizaable algebras (the algebraization of the theories which express Theor; II), to appear inBolletino della Unione Matematica Italiana.

  9. R. Magari,Representation and duality theory for diagonalizable algebras (the algebraization of the theories which express Theor; IV),Studia Logica, Vol. 34, No. 4, pp. 305–315.

  10. G. Marongiu,Sequenze di predicati aritmetici di tipo teor,Bolletino della Unione Matematica Italiana, Vol. IX (1974), pp. 361–375.

    Google Scholar 

  11. P. Pagli,On some extensions of diagonalization lemma in Lindenbaum algebra of Peano arithmetic (the algebraization of theories which express Theor; 1), to appear.

  12. G. Sambin,Un'estensione del teorema di Löb, to appear inRendiconti del Seminario Matematico dell Universitá di Padova.

  13. G. Sambin,An effective fixed-point theorem in the intuitionistic diagonalizable algebras,Studia Logica, Vol. 35 No 4, pp. 345–363.

  14. H. Simmons,Topological aspects of suitable theories, mimeographed 1972.

  15. C. Smoryński,Consistency statements and related metamathematical properties,Report 75-02, Department of Mathematics, University of Amsterdam 1975.

  16. C. Smoryński,The incompleteness theorems, to appear.

Download references

Author information

Authors and Affiliations

  1. Siena University, Siena, Italy

    Franco Montagna

Authors
  1. Franco Montagna
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Allatum est die 24 Maii 1976

Rights and permissions

Reprints and permissions

About this article

Cite this article

Montagna, F. On the algebraization of a Feferman's predicate. Stud Logica 37, 221–236 (1978). https://doi.org/10.1007/BF02124724

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02124724

Keywords

Search

Navigation