## Notre Dame Journal of Formal Logic

### The Contribution of Zygmunt Ratajczyk to the Foundations of Arithmetic

Roman Murawski

#### 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

https://projecteuclid.org/euclid.ndjfl/1040136911

Digital Object Identifier
doi:10.1305/ndjfl/1040136911

Mathematical Reviews number (MathSciNet)
MR1368462

Zentralblatt MATH identifier
0844.03001

#### 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

#### References

• “On extendability of uncountable nonstandard models of ZF to models of KM," abstract, The Journal of Symbolic Logic, vol. 42 (1977), p. 466.
• “On sentences provable in impredicative extensions of theories," Dissertationes Mathematicæ, vol. 178 (1979), pp. 1–44. Zbl 0427.03041 MR 81g:03062
• “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. Zbl 0445.03028 MR 83j:03056
• “A characterization of expandability of models for ZF to models for KM," Fundamenta Mathematicæ, vol. 113 (1981), pp. 9–19. Zbl 0478.03015 MR 83b:03041
• “Satisfaction classes and combinatorial sentences independent from PA," Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 28 (1982), pp. 149–165. Zbl 0522.03043 MR 83j:03097
• “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.
• “Traces of models on initial segments," abstract, The Journal of Symbolic Logic, vol. 50 (1985), pp. 273–274.
• “A combinatorial analysis of functions provably recursive in $I\Sigma_{n}$," Fundamenta Mathematicæ, vol. 130 (1988), pp. 191–213. Zbl 0659.03036 MR 90d:03126
• “Functions provably total in $I^{-}\Sigma_{n}$," Fundamenta Mathematicæ, vol. 133 (1989), pp. 81–95. Zbl 0703.03018 MR 91k:03140
• (with H. Kotlarski) “Inductive full satisfaction classes," Annals of Pure and Applied Logic, vol. 47 (1990), pp. 199–223. Zbl 0708.03014 MR 92b:03058
• (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. Zbl 0723.03033 MR 92b:03059
• “The Frege systems in the language of clauses," abstract, The Journal of Symbolic Logic, vol. 56 (1991), p. 1140.
• “Arithmetical transfinite induction and hierarchies of functions," Fundamenta Mathematicæ, vol. 141 (1992), pp. 1–20. Zbl 0809.03043 MR 93i:03081
• “Subsystems of true arithmetic and hierarchies of functions," Annals of Pure and Applied Logic, vol. 64 (1993), pp. 95–152. Zbl 0802.03036 MR 94f:03068