For sentences of , we investigate the question of absoluteness of having models in uncountable cardinalities. We first observe that having a model in is an absolute property, but having a model in is not as it may depend on the validity of the continuum hypothesis. We then consider the generalized continuum hypothesis (GCH) context and provide sentences for any for which the existence of a model in is nonabsolute (relative to large cardinal hypotheses). Finally, we present a complete sentence for which model existence in is nonabsolute.
"The Nonabsoluteness of Model Existence in Uncountable Cardinals for ." Notre Dame J. Formal Logic 54 (2) 137 - 151, 2013. https://doi.org/10.1215/00294527-1960443