Small inductive dimension and universality on frames
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In this paper we prove that for a fixed integer or an ordinal \(\alpha \) and a fixed infinite cardinal \(\tau \) the class of all regular frames of weight less than or equal to \(\tau \) with small inductive dimension less than or equal to \(\alpha \) is saturated and therefore, in this class of frames there exist universal elements.
KeywordsSmall inductive dimension of frames Universal frame Saturated class of frames
Mathematics Subject Classification06A06 06D22 06F30 54H12 54F05
The authors would like to thank the referee for the careful reading of the paper and the useful comments. The fourth author of the paper F. Sereti (with scholarship code 2547) would like to thank the General Secretariat for Research and Technology (GSRT) and the Hellenic Foundation for Research and Innovation (HFRI) for the financial support of this study.
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