In FOL, a formula is interpreted in meta-language as $m,s\models\phi$, where m is a model/structure and s is an assignment function. If we continue to interpret this meta-language sentence, how can we do? How to determine a domain? I think this domain should at least include some models, some assignment functions, and some FOL formulas. This seems quite different from the domain we choose to interpret an FOL formula, which contains things of the same kind. The objects in the domain for the meta-language belong to various kinds(models, assignment functions, FOL formulas, etc.) Am I on the wrong way?
2026-04-12 13:29:19.1776000559
How to interpret formulas in meta-language?
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