An application of a reflection principle

Volume 180 / 2003

Zofia Adamowicz, Leszek Aleksander Kołodziejczyk, Paweł Zbierski Fundamenta Mathematicae 180 (2003), 139-159 MSC: Primary 03F30. DOI: 10.4064/fm180-2-2


We define a recursive theory which axiomatizes a class of models of $I\Delta _0 + \Omega _3 + \neg \mathop {\rm exp}\nolimits $ all of which share two features: firstly, the set of $\Delta _0$ definable elements of the model is majorized by the set of elements definable by $\Delta _0$ formulae of fixed complexity; secondly, $\Sigma _1$ truth about the model is recursively reducible to the set of true $\Sigma _1$ formulae of fixed complexity.


  • Zofia AdamowiczInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
  • Leszek Aleksander KołodziejczykInstitute of Philosophy
    Warsaw University
    Krakowskie Przedmieście 3
    00-047 Warszawa, Poland
  • Paweł Zbierski(deceased; 1944-2002)

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