The length of chains in algebraic lattices
| dc.creator | Chakir, Ilham | |
| dc.creator | Pouzet, Maurice | |
| dc.date | 2008-12-11 | |
| dc.date.accessioned | 2026-07-07T12:12:03Z | |
| dc.date.available | 2026-07-07T12:12:03Z | |
| dc.description | We study how the existence in an algebraic lattice $L$ of a chain of a given type is reflected in the join-semilattice $K(L)$ of its compact elements. We show that for every chain $α$ of size $κ$, there is a set $\B$ of at most $2^κ$ join-semilattices, each one having a least element such that an algebraic lattice $L$ contains no chain of order type $I(α)$ if and only if the join-semilattice $K(L)$ of its compact elements contains no join-subsemilattice isomorphic to a member of $\B$. We show that among the join-subsemilattices of $[ω]^{<ω}$ belonging to $\B$, one is embeddable in all the others. We conjecture that if $α$ is countable, there is a finite set $\B$. | |
| dc.description | 11 pages, 2 figures, Proceedings ISOR'08, Algiers, Nov. 2-6, 2008 | |
| dc.identifier | https://arxiv.org/abs/0812.2193 | |
| dc.identifier | http://arxiv.org/abs/0812.2193 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210423 | |
| dc.subject | Combinatorics | |
| dc.subject | Logic | |
| dc.subject | 06A12, 06B35 | |
| dc.title | The length of chains in algebraic lattices | |
| dc.type | text |