Discussion on question by PL_OLCOTT: How could the Tarski Undefinability Theorem be Refuted?

That it applies to arithmetic "and above" is written in Wikipedia, so it can't be that unknown. But if you think this means "applies to all of math" you are very naive about how theorems work. "Definable in mathematics" is not exactly reassuring either. Tarski proved a technical result about a class of formal languages, not "all of math", and so far you displayed little awareness of what the technical conditions are.

"It" is not the language Tarski used, so his theorem is not obligated to apply. And "any proof that this does not work seems to fail" is very strangely phrased. There supposed to be a proof that it does work (whatever "work" means here), and if you think there is one submit it for peer review, instead of wasting time on a Q&A site.

@Conifold I refer you to this exchange on math.stackexchange. I'm not convinced this discussion will be of any use, unfortunately.