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Archive for Mathematical Logic

, Volume 32, Issue 6, pp 391–398 | Cite as

Interpretations of the alternative set theory

  • A. Sochor
Article

Summary

We show an axiom A such that there is no nontrivial interpretation of the alternative set theory (AST) inAST+A keeping ∈, sets and the class of all “standard” natural numbers. Furthermore, there is no interpretation ofAST inAST without the prolongation axiom, but there is an interpretation ofAST in the theory having the prolongation axiom and the basic set-theoretical axioms only.

Mathematicals subject classification (1991)

03E70 03E35 03F35 

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References

  1. [Č-S-Z] Čuda, K., Sochor, A., Zlatoš, P.: Guide to alternative set theory. In: Mlček, J., Benešová, M., Vojtášková, B. (eds.), Proceedings of the 1st Symposium Mathematics in the alternative set theory, pp. 44–138. Union of Slovak Mathematicians and Physicists, Bratislava 1989Google Scholar
  2. [S1] Sochor, A.: Metamathematics of the alternative set theory II. Commentat. Math. Univ. Carol.23, 55–79 (1982)Google Scholar
  3. [S2] Sochor, A.: Constructibility in higher order arithmetics. Arch. Math. Logik32, 381–389 (1993)Google Scholar
  4. [S3] Sochor, A.: Choices of convenient sets. (to appear)Google Scholar
  5. [S-V] Sochor, A., Vopěnka, P.: Shiftings of the horizon. Commentat. Math. Univ. Carol.24, 127–136 (1983)Google Scholar
  6. [V] Vopěnka, P.: Mathematics in the Alternative Set Theory. Leipzig: Teubner Texte 1979Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • A. Sochor
    • 1
  1. 1.Mathematical InstituteAcademy Sciences of Czech RepublicPrague 1Czech Republic

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