The question is in regards to The Lowenheim-Skolem theorem and the question asks to give a set of sentences that is only true in an uncountable domain. My teacher told me to solve this by "relaxing" the conditions on the language of first order logic so that it is uncountable.
Because the question asks to give a set of sentences in an uncountable domain this leads me to believe that I should try to make either the set of countably infinite constants and/or countably infinite variables uncountable, in the language, but i'm stuck on how to do this and apply it so there's sentences that are only true in this uncountable domain. Any help is appreciated.