# What does it mean: “the closure of the axioms”?

«As we shall see, the logical axioms are so designed that the logical consequences (in the semantic sense, cf. p. 56) of the closure of the axioms of $K$ are precisely the theorems of $K$.» Page 60 “Introduction to Mathematical Logic“ SECOND EDITION by ELLIOTT MENDELSON The same is in fourth edition.

What does it mean: “the closure of the axioms”?

-
When you say "the same is in the fourth edition", is it located elsewhere (not p.60) of the fourth edition, I searched on line, found 4th ed., but there is no statement there resembling the statement you're interested in. I suspect more is meant by "the logical consequence...of the closure of the axioms of K are precisely the theorems of K" than closure of a particular formula whose variables are bound by a universal quantifier... – amWhy May 20 '11 at 23:45
See "universal closure" here en.wikipedia.org/wiki/… – Bill Dubuque May 30 '11 at 20:53