# Misprint in “Mathematical Logic” by Stephen Cole Kleene

Page 18 “Theorem 3. If $\models A$ and $\models A\to B$, then $\models B$.”

Page 43 From prove of Theorem 12. “By Theorem 3, given that premises $A$ and $B$ for an application of modus ponens are valid, so is the conclusion $B$.”

It is looks to me as misprint. It should be “By Theorem 3, given that premises $A$ and $A\to B$ for an application of modus ponens are valid, so is the conclusion $B$.”

Am I right?

• Luckily Google books had enough of a preview for me to check. Yes, you are right. – André Nicolas Aug 12 '11 at 0:25

In order not to leave this question unanswered, I will turn my earlier comment into an answer.

Yes, you are right, it definitely should be $A\to B$, and not simply $B$. Minor slip.

Luckily, Google books gave a generous preview, so I was able to see the entire context: there is no doubt.

Dover does not seem to maintain an errata file, and there is nothing on the web site of the original publisher (Wiley).

• "Given that premises A and A→B for an application of modus ponens are valid, so is the conclusion B.” is that to be read as (A and A→B) entails B, or (A and A→B) implies B? – alancalvitti Dec 13 '12 at 3:43