The variety of Brouwerian semilattices is amalgamable and locally finite, hence by well-known results [Whe76], it has a model completion (whose models are the existentially closed structures). In this paper, we supply for such a model completion a finite and rather simple axiomatization.2010 Mathematics subject classification. Primary 03G25; Secondary 03C10, 06D20.A co-Brouwerian semilattice, CBS for short, is a structure obtained by reversing the order of a Brouwerian semilattice. We will work with CBSes instead of Brouwerian semilattices.Definition 2.1. A poset (P, ≤) is said to be a co-Brouwerian semilattice if it has a least element, which we denote with 0, and for every a, b ∈ P there exists the sup of {a, b}, which we call join of a and b and denote with a ∨ b, and the difference a − b satisfying for every c ∈ PClearly, there is also an alternative equational definition for co-Brouwerian semilattices (which we leave to the reader, because it is dual to the equational definition for Brouwerian semilattices given above).Moreover, we will call co-Heyting algebras the structures obtained reversing the order of Heyting algebras. Obviously any co-Heyting algebra is a CBS.Definition 2.2. Let A, B be co-Brouwerian semilattices. A map f : A → B is a morphism of co-Brouwerian semilattices if it preserves 0, the join and difference of any two elements of A.Notice that such a morphism f is an order preserving map because, for any a, b elements of a co-Brouwerian semilattice, we have a ≤ b iff a ∨ b = b.Definition 2.3. Let L be a CBS. We say that g ∈ L is join-irreducible iff for every n ≥ 0 and b 1 , . . . , b n ∈ L, we have that g ≤ b 1 ∨ . . . ∨ b n implies g ≤ b i for some i = 1, . . . , n.Notice that taking n = 0 we obtain that join-irreducibles are different from 0.Remark 2.4. Let L be a CBS and g ∈ L. Then the following conditions are equivalent:1. g is join-irreducible.2. g = 0 and for any b 1 , b 2 ∈ L we have that g3. For every n ≥ 0 and b 1 , . . . , b n ∈ L we have that g = b 1 ∨ . . . ∨ b n implies g = b i for some i = 1, . . . , n.4. g = 0 and for any b 1 , b 2 ∈ L we have that g = b 1 ∨ b 2 implies g = b 1 or g = b 2 .5. g = 0 and for any a ∈ L we have that g − a = 0 or g − a = g.Proof. The implications 1 ⇔ 2, 3 ⇔ 4 and 1 ⇒ 3 are straightforward. For the remaining ones see Lemma 2.1 in [Köh81].Definition 2.5. Let L be a CBS and a ∈ L.A join-irreducible component of a is a maximal element among the join-irreducibles of L that are smaller than or equal to a.