#### nomadreid

Gold Member

- 1,288

- 103

Given that, I would like to know if the following is a correct way to look at phrases such as "the cardinality of the set of constant symbols of a language."

(1) One can only make this phrase in reference to a new model in which the (previous) constant symbols become constants, so that this collection can be a set.

(2) The collection of constants in the universe of the new model must be larger than the universe of the original model, because there is nothing to stop one having one constant symbol (in the original theory) for every constant in the universe (of the original model), and a collection that is as large as the universe cannot be a set.

Please correct the faults in the above. Thanks.