# Notes on Cardinals That Are Characterizable by a Complete (Scott) Sentence

@article{Souldatos2014NotesOC, title={Notes on Cardinals That Are Characterizable by a Complete (Scott) Sentence}, author={Ioannis A. Souldatos}, journal={Notre Dame J. Formal Log.}, year={2014}, volume={55}, pages={533-551} }

This is part I of a study on cardinals that are characterizable by Scott sentences. Building on [3], [6] and [1] we study which cardinals are characterizable by a Scott sentence $\phi$, in the sense that $\phi$ characterizes $\kappa$, if $\phi$ has a model of size $\kappa$, but no models of size $\kappa^+$. We show that the set of cardinals that are characterized by a Scott sentence is closed under successors, countable unions and countable products (cf. theorems 2.3, 3.4, and corollary 3.6…

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