### Title

*Exact and quasi-exact universal models for fragments of intuitionistic propositional logic*

### Abstract

Intuitionistic propositional logic, envisaged as the free Heyting algebra over a non-empty collection of generators P, is infinite. When P is a singleton, we obtain the
well-known Riegerâ€“Nishimura lattice. For larger P, however, the free Heyting algebra is very complex and little is known about it. Closer inspection learns that the
combination of disjunction and implication causes the free Heyting algebras to become infinite. When we only consider formulae of IpL without disjunction, the corresponding
algebras are finite. However, as N.G. de Bruijn already pointed out, their size grows superexponentially with the number of generators. I will report on investigations on
fragments of IpL without disjunction. For the characterization of these fragments, (quasi-)exact models are used, a special kind of universal models. The presentation is
based on joint work with Dick de Jongh and Lex Hendriks.

### References

http://logcom.oxfordjournals.org/cgi/reprint/exq058?ijkey=s85AtbYEq6ckd9r&keytype=ref