Archive for Mathematical Logic

, Volume 54, Issue 7–8, pp 741–767

# On the share of closed IL formulas which are also in GL

Article

## Abstract

Normal forms for wide classes of closed IL formulas were given in Čačić and Vuković (Math Commun 17:195–204, 2012). Here we quantify asymptotically, in exact numbers, how wide those classes are. As a consequence, we show that the “majority” of closed IL formulas have GL-equivalents, and by that, they have the same normal forms as GL formulas. Our approach is entirely syntactical, except for applying the results of Čačić and Vuković. As a byproduct we devise a convenient way of computing asymptotic behaviors of somewhat general classes of formulas given by their grammar rules. Its applications do not require any knowledge of the recurrence relations, generating functions, or the asymptotic enumeration methods, as all these are incorporated into two fundamental parameters.

### Keywords

Interpretability logic Normal forms Asymptotic enumeration

03F05 05A16

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