Sep 2026· Bulletin of the Section of Logic· 0 citations
Abstract
We show that partially ordered sets, lattices, semilattices, Boolean algebras, Heyting algebras with a further coarser or finer partial order, or a linearization, or an auxiliary relation have the strong amalgamation property, Fraïssé limits and, in many cases, an \(\omega\)-categorical model completion with quantifier elimination.
The same applies to causal spaces, introduced by Kronheimer and Penrose in connection with foundational problems in general relativity. Our main tool is the superamalgamation property, thus we provide arguments suggesting the usefulness of the superamalgamation property also in pure model theory, not only in algebraic logic.
Looking at some monoids and (semi)rings (natural numbers, integers and $p$-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function $f$ on such an algebra to behave like the operations of the algebra. The first way is to preserve congruences...
We prove that Brandt semirings over nontrivial groups with at least two indices admit no identity basis with a bounded number of variables. A uniform family of finite witnesses has size linear in the variable bound and applies to groups of arbitrary cardinality. A commutative construction yields the corresponding resul...
For simple, nonelementary C*-algebras, we show uniform density of functions realized as ranks of operators. It follows that strict comparison by traces forces almost divisibility, and hence pureness. As an application, we show that strict comparison implies $\mathcal{Z}$-stability for separable, simple, nonelementary C...
The monoidal product \(\odot\) of an MV-algebra determines an annihilation relation that differs from the classical lattice polar. On order ideals, iteration of the corresponding annihilator twice produces a closure operator. Its fixed points are compared with zero-productabsorbing, ⊙ -semiprime, and ⊙ -prime order ide...
C. Park· Far East Journal of Mathemat...· 0 citations
We answer the question whether all Heyting algebras can appear as the lattice of subterminal objects of an elementary topos in the negative. Concretely, we show that the free Heyting algebra on two generators, hence also on N generators for every N greater than 2, cannot be such a Heyting algebra. The mathematical resu...
We study the profinite non-rigidity of arithmetic lattices and its implications for the K\"ahler property. In the first part, we characterize the absolute Dynkin types that admit non-isomorphic real forms of higher-rank Lie groups containing torsion-free arithmetic lattices with isomorphic profinite completions. In the...
Yu-Kun Du, F. Hao, Ke-Jia Zhu· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
