Talk:Truth-value semantics

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[edit] Theorem of Beth

I'm interested to read about the theorem of Beth alluded to in the article. It certainly isn't true that in ordinary first-order logic, anonymous elements of the domain can be ignored; for example the real numbers satisfy in the language of rings, but there is no constant symbol for either root. So I am curious what context Beth was working in that made it possible to avoid this issue. — Carl (CBM · talk) 13:15, 3 May 2008 (UTC)

Technically there is a restriction on the size of the set of individual constants for the theorem to hold, viz. by Lowenheim-Skolem theorem, at least aleph-null. As per your particular example, the article is misleading, since the theorem pertains, not to satisfiability I think, but validity. Nortexoid (talk) 21:16, 4 May 2008 (UTC)

Yes, the article is misleading. I'd like to fix it, but I don't know what it's trying to say. I'm just going to remove that sentence for now, we can always add it later if we figure out how to correct it. — Carl (CBM · talk) 21:17, 4 May 2008 (UTC)