Hristo Ganchev | Searcharxiv

arXiv2026

Intuitionism and computing with partial information

There exist initial segments of both the Dyment lattice and the Dyment-Muchnik lattice that yield Brouwer algebras modeling exactly the intuitionistic propositional calculus. For the Dyment-Muchnik lattice, this result is obtained by constructing a splitting class of enumeration degrees. In contrast, the full Dyment lattice and the full Dyment-Muchnik lattice model the intuitionistic propositional calculus plus the weak law of excluded middle. We also observe that certain naturally definable classes of enumeration degrees, which are downwards closed under enumeration reducibility, fail to form splitting classes.

math.LO↗

arXiv2021

Computable embeddings for pairs of linear orders

We study computable embeddings for pairs of structures, i.e. for classes containing precisely two non-isomorphic structures. Surprisingly, even for some pairs of simple linear orders, computable embeddings induce a non-trivial degree structure. Our main result shows that $\{ω\cdot k,ω^\star \cdot k\}$ is computably embeddable in $\{ω\cdot t, ω^\star \cdot t\}$ iff $k$ divides $t$.

math.LO↗