Skip to main content
SpringerLink
Log in

On the autological character of diagonalizable algebras

  • Articles
  • Published:
Studia Logica Aims and scope Submit manuscript

Summary

Let ℱ be the first order theory of diagonalizable algebras. We define a bijection ϕ from the atomic formulas of ℱ (identities) to the open formulas of ℱ. ϕ is an algebraic analogous of ≒. We prove that ϕ, ϕ-1 preserve the validity.

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 the diagonalizable algebras (the algebraization of the theories which express Theor; III),Studia Logica XXXIV 3 (1975), pp. 239–251.

    Article  Google Scholar 

  2. C. Bernardi,On the equational class of diagonalizable algebras (the algebraization of the theories which express Theor, VI),Studia Logica XXXIV, 4 (1975), pp. 321–331.

    Article  Google Scholar 

  3. R. Magari,The diagnonalizable algebras (the algebraization of the theories which express Theor; II),Bollettino Unione Matematica Haliana 12 (1975), pp. 117–125.

    Google Scholar 

  4. R. Magari,Representation and duality theory for diagonalizable algebras (the algebraization of the theories, which express Theor; IV) Studia Logica XXXIV, 4 (1975), pp. 305–313.

    Article  Google Scholar 

  5. E. Mendelson,Introduction to mathematical logic, D. Van Nostrand Company, Princeton, New Jersey, 1964.

    Google Scholar 

  6. F. Montagna,For every n, the n-freely generated algebra is, not functionally free in the equational class of diagonalizable algebras (the algebraization of the theories which express Theor; V).Studia Logica XXXIV. 4 (1975), pp. 315–319.

    Article  Google Scholar 

  7. P. Pagli,Su alcune estensioni del lemma di diagonalizzazione nell'aritmetica di Peano, to appear.

  8. H. Rasiowa andR. Sikorski,The mathematics of metamathematics, Warszawa, PWN, 1963.

    Google Scholar 

  9. R. Sikorski,Boolean algebras, Springer-Verlag, Berlin-Heidelberg-New York 1963 (third edition).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Siena University, Italy

    Roberto Magari

Authors
  1. Roberto Magari
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The algebraization of the theories which express Theor

See the precedent papers with the same subtitle.

Allatum est die 21 Julii 1975

Rights and permissions

Reprints and permissions

About this article

Cite this article

Magari, R. On the autological character of diagonalizable algebras. Stud Logica 35, 327–333 (1976). https://doi.org/10.1007/BF02123400

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02123400

Keywords

Search

Navigation