Geodesic
An application of a reflection principle
Zofia Adamowicz 1   ; Leszek Aleksander Kołodziejczyk 2   ; Paweł Zbierski 3
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland
2 Institute of Philosophy Warsaw University Krakowskie Przedmieście 3 00-047 Warszawa, Poland
3 (deceased; 1944-2002)
Fundamenta Mathematicae, Tome 180 (2003) no. 2, pp. 139-159 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm180-2-2
Keywords: define recursive theory which axiomatizes class models delta omega neg mathop exp nolimits which share features firstly set delta definable elements model majorized set elements definable delta formulae fixed complexity secondly sigma truth about model recursively reducible set sigma formulae fixed complexity

Zofia Adamowicz  1   ; Leszek Aleksander Kołodziejczyk  2   ; Paweł Zbierski  3

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland
2 Institute of Philosophy Warsaw University Krakowskie Przedmieście 3 00-047 Warszawa, Poland
3 (deceased; 1944-2002) 
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Zofia Adamowicz; Leszek Aleksander Kołodziejczyk; Paweł Zbierski. An application of a reflection principle. Fundamenta Mathematicae, Tome 180 (2003) no. 2, pp. 139-159. doi: 10.4064/fm180-2-2

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