Notre Dame Journal of Formal Logic

The Contribution of Zygmunt Ratajczyk to the Foundations of Arithmetic

Roman Murawski

Full-text: Open access

Enhanced PDF (29 KB) PDF File (22 KB)

Abstract

Zygmunt Ratajczyk was a deep and subtle mathematician who, with mastery, used sophisticated and technically complex methods, in particular combinatorial and proof-theoretic ones. Walking always along his own paths and being immune from actual trends and fashions he hesitated to publish his results, looking endlessly for their improvement.

Article information

Source
Notre Dame J. Formal Logic Volume 36, Number 4 (1995), 502-504.

Dates
First available in Project Euclid: 17 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1040136911

Digital Object Identifier
doi:10.1305/ndjfl/1040136911

Mathematical Reviews number (MathSciNet)
MR1368462

Zentralblatt MATH identifier
0844.03001

Subjects
Primary: 01A70: Biographies, obituaries, personalia, bibliographies
Secondary: 03-03: Historical (must also be assigned at least one classification number from Section 01) 03C62: Models of arithmetic and set theory [See also 03Hxx]

Citation

Murawski, Roman. The Contribution of Zygmunt Ratajczyk to the Foundations of Arithmetic. Notre Dame J. Formal Logic 36 (1995), no. 4, 502--504. doi:10.1305/ndjfl/1040136911. https://projecteuclid.org/euclid.ndjfl/1040136911.


Export citation

References

  • [1] ``On extendability of uncountable nonstandard models of ZF to models of KM," abstract, The Journal of Symbolic Logic, vol. 42 (1977), p. 466.
  • [2] ``On sentences provable in impredicative extensions of theories," Dissertationes Mathematicæ, vol. 178 (1979), pp. 1--44.
    Mathematical Reviews (MathSciNet): MR81g:03062
    Zentralblatt MATH: 0427.03041
  • [3] ``On the number of expansions of the models of ZFC-set theory to models of KM-theory of classes," pp. 317--333 in Logic Colloquium '78, edited by M. Boffa, D. van Dalen, and K. McAloon, North-Holland, Amsterdam, 1979.
    Mathematical Reviews (MathSciNet): MR83j:03056
    Zentralblatt MATH: 0445.03028
  • [4] ``A characterization of expandability of models for ZF to models for KM," Fundamenta Mathematicæ, vol. 113 (1981), pp. 9--19.
    Mathematical Reviews (MathSciNet): MR83b:03041
    Zentralblatt MATH: 0478.03015
  • [5] ``Satisfaction classes and combinatorial sentences independent from PA," Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 28 (1982), pp. 149--165.
    Mathematical Reviews (MathSciNet): MR83j:03097
    Zentralblatt MATH: 0522.03043
    Digital Object Identifier: doi:10.1002/malq.19820280804
  • [6] ``Note on submodels for A$_2$," pp. 265--280 in Open Days in Model Theory and Set Theory, edited by W. Guzicki, W. Marek, A. Pelc and C. Rauszer, Leeds, 1983.
  • [7] ``Traces of models on initial segments," abstract, The Journal of Symbolic Logic, vol. 50 (1985), pp. 273--274.
  • [8] ``A combinatorial analysis of functions provably recursive in $I\Sigma_n$," Fundamenta Mathematicæ, vol. 130 (1988), pp. 191--213.
    Mathematical Reviews (MathSciNet): MR90d:03126
    Zentralblatt MATH: 0659.03036
  • [9] ``Functions provably total in $I^-\Sigma_n$," Fundamenta Mathematicæ, vol. 133 (1989), pp. 81--95.
    Mathematical Reviews (MathSciNet): MR91k:03140
    Zentralblatt MATH: 0703.03018
  • [10] (with H. Kotlarski) ``Inductive full satisfaction classes," Annals of Pure and Applied Logic, vol. 47 (1990), pp. 199--223.
    Mathematical Reviews (MathSciNet): MR92b:03058
    Zentralblatt MATH: 0708.03014
    Digital Object Identifier: doi:10.1016/0168-0072(90)90035-Z
  • [11] (with H. Kotlarski) ``More on induction in the language with a satisfaction class," Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 36 (1990), pp. 441--454.
    Mathematical Reviews (MathSciNet): MR92b:03059
    Zentralblatt MATH: 0723.03033
    Digital Object Identifier: doi:10.1002/malq.19900360509
  • [12] ``The Frege systems in the language of clauses," abstract, The Journal of Symbolic Logic, vol. 56 (1991), p. 1140.
  • [13] ``Arithmetical transfinite induction and hierarchies of functions," Fundamenta Mathematicæ, vol. 141 (1992), pp. 1--20.
    Mathematical Reviews (MathSciNet): MR93i:03081
    Zentralblatt MATH: 0809.03043
  • [14] ``Subsystems of true arithmetic and hierarchies of functions," Annals of Pure and Applied Logic, vol. 64 (1993), pp. 95--152.
    Mathematical Reviews (MathSciNet): MR94f:03068
    Zentralblatt MATH: 0802.03036
    Digital Object Identifier: doi:10.1016/0168-0072(93)90031-8

Duke University Press

Notre Dame Journal of Formal Logic

New content alerts

Email RSS ToC RSS Article
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more