Comment on Mental Context for Model Theory

Fri, 01 Nov 2013 02:10:57 GMT

The operations on a Rubix cube aren't abelian. Is that just a typo on your part, or am I missing some subtle point you are making?

I'm not sure what you are getting at when you say you don't want to found math on sets. I definitely intended to use the word "set" in a naive sense, so that it is perfectly fine for sets to contain numbers, or rotations of a Rubix cube, or for that matter rocks and flowers. I wasn't trying to imply that the elements of a model had to be recursively constructed from the nullset by the axioms of ZFC. If you prefer "collection of things", I'd be glad to go with that. But I (and more to the point, model theorists) do want to think of a model as a bunch of objects with functions that take as inputs these objects and make other objects, and relations which do and do not hold between various pairs of the objects.

I'm retracting a bunch of the other things I wrote after this because, on reflection, the later material was replying to a misreading of what you wrote in your following post. I still think your de-emphasis on the fact that the model is the universe is very confusing, especially when you then talk about the cardinality of models. (What is the cardinality of a rule for assigning truth values?) But on careful reading, you weren't actually saying something wrong.

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