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We consider compactness characterizations of large cardinals. Based on results of Benda [Ben78], we study compactness for omitting types in various logics. In $$\mathbb{L}$$ L κ,κ , this allows us… Click to show full abstract
We consider compactness characterizations of large cardinals. Based on results of Benda [Ben78], we study compactness for omitting types in various logics. In $$\mathbb{L}$$ L κ,κ , this allows us to characterize any large cardinal defined in terms of normal ultrafilters, and we also analyze second-order and sort logic. In particular, we give a compactness for omitting types characterization of huge cardinals, which have consistency strength beyond Vopĕnka’s Principle.
Keywords:
large cardinals;
compactness;
characterizations large;
theoretic characterizations;
model theoretic
Journal Title: Israel Journal of Mathematics
Year Published: 2017
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Journal Title: Israel Journal of Mathematics
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!