They distinguish between the syntactic content of a theory (the axioms of the theory) and its semantic content (the models for which those axioms hold).
How confusing. I do see this terminology used in a Wikipedia article that I don’t really understand, but I would call sequences like [For, any, two, points, exactly, one, line, lies, on, both] the syntax. The axioms would be the “semantic” content (...or simply “the axioms”), and the models for which the axioms hold the “domain” or “scope”.
How confusing. I do see this terminology used in a Wikipedia article that I don’t really understand, but I would call sequences like [For, any, two, points, exactly, one, line, lies, on, both] the syntax. The axioms would be the “semantic” content (...or simply “the axioms”), and the models for which the axioms hold the “domain” or “scope”.