H. L. M. (Hrushovski-Lang-Mordell)
Hanf numbers and well-ordering numbers.
Herbrand consistency and bounded arithmetic
We prove that the Gödel incompleteness theorem holds for a weak arithmetic Tₘ = IΔ₀ + Ωₘ, for m ≥ 2, in the form Tₘ ⊬ HCons(Tₘ), where HCons(Tₘ) is an arithmetic formula expressing the consistency of Tₘ with respect to the Herbrand notion of provability. Moreover, we prove , where is HCons relativised to the definable cut Iₘ of (m-2)-times iterated logarithms. The proof is model-theoretic. We also prove a certain non-conservation result for Tₘ.
Hierarchies and reducibilities on regular languages related to modulo counting
We discuss some known and introduce some new hierarchies and reducibilities on regular languages, with the emphasis on the quantifier-alternation and difference hierarchies of the quasi-aperiodic languages. The non-collapse of these hierarchies and decidability of some levels are established. Complete sets in the levels of the hierarchies under the polylogtime and some quantifier-free reducibilities are found. Some facts about the corresponding degree structures are established. As an application,...
Hierarchies and reducibilities on regular languages related to modulo counting
We discuss some known and introduce some new hierarchies and reducibilities on regular languages, with the emphasis on the quantifier-alternation and difference hierarchies of the quasi-aperiodic languages. The non-collapse of these hierarchies and decidability of some levels are established. Complete sets in the levels of the hierarchies under the polylogtime and some quantifier-free reducibilities are found. Some facts about the corresponding degree structures are established. As an application, we...
Homogeneity, universality and saturatedness of limit reduced powers (II)
Homogeneity, universality and saturatedness of limit reduced powers III
Homogeneity, universality and saturatedness of limit reduced powers I
Homogeneous limit reduced powers.
Homogeneous models and generic extensions.
Homogeneous models and stable diagrams.
Homogeneous permutations.
Homogeneous-Universal Models of Theories Which Have Model Completions
Homological Dimension and representation type of algebras under base field extension.
Hyperarithmetical Boolean algebras with a distinguished ideal.
Hyperidentities in associative graph algebras
Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity s ≈ t if the correspondinggraph algebra A(G) satisfies s ≈ t. A graph G is called associative if the corresponding graph algebra A(G) satisfies the equation (xy)z ≈ x(yz). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A̲ if whenever the operation symbols occurring in s and t are replaced...
Hypersatisfaction of formulas in agebraic systems
In [2] the theory of hyperidentities and solid varieties was extended to algebraic systems and solid model classes of algebraic systems. The disadvantage of this approach is that it needs the concept of a formula system. In this paper we present a different approach which is based on the concept of a relational clone. The main result is a characterization of solid model classes of algebraic systems. The results will be applied to study the properties of the monoid of all hypersubstitutions of an...