2
$\begingroup$

«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”?

  • 0
    S$e$e "universal closure" here http://en.wikipedia.org/wiki/Universal_quantification#universal_closure2011-05-30

1 Answers 1

1

Maybe: the closure of a formula means universally quantifying over all its free variables? And perhaps this definition is somewhere before page 60?

Edit. Look in the index under: closure, (universal) of a formula

  • 0
    @Victor Victorov: Similarly, in lambda calculu$s$ to close a term means to bind all its free variables with abstraction. In logic — with universal quantifier. Not a good term though, because closure ma$y$ be deductive closure as well.2011-08-27