arXiv subjects
Publications and source records attributed to Luiz F. Monteiro.
Five-valued Nelson algebras are those satisfying the condition: $((x\to z)\to y)\to(((y \to x)\to y)\to y)=1$. We give alternative equations defining these algebras, and determine the structure and number of elements of the free five-valued Nelson algebra with a finite number of free generators.
Let $P(n)$ be the set of all posets with $n$ elements. Let $P^{(j)}(n)$, $1\leq j\leq 2^n,$ be the number of all posets with $n$ elements possessing exactly $j$ antichains. We have determined the numbers $P^{(j)}(7),$ $1\leq j\leq 128$, and using a result of M.~Erné [Erné, M., On the cardinalities of finite topologies and the number of antichains in partially ordered sets, Discrete Mathematics 35 (1981), 119-133.], we compute $|P(10)|$ without the aid of any computer program. We include the Hasse diagrams of all the non-isomorphic posets of $P(7)$. We also present formulas for the number of connected posets of certain forms, and use them to compute $|P(n)|$ with $1\le n\le 8$ by a different method.
We provide a recursive construction of all the semi-Heyting algebras that can be defined on a chain with $n$ elements. This construction allows us to count them easily. We also compare the formula for the number of semi-Heyting chains thus obtained to the one previously known.