Equational Bases for Lattice Theories.
-incompactness of Z
Cardinal multiplication of structures with a reflexive relation
Einstein metrics and quaternionic Kähler manifolds.
Toward an arithmetic of polynomials.
Definability in the lattice of equational theories of semigroups.
Powers of partially ordered sets: Cancellation and reffinement properties.
k-ary monoids of term operations.
Affine Parikh automata
The Parikh finite word automaton (PA) was introduced and studied in 2003 by Klaedtke and Rueß. Natural variants of the PA arise from viewing a PA equivalently as an automaton that keeps a count of its transitions and semilinearly constrains their numbers. Here we adopt this view and define the , that extends the PA by having each transition induce an affine transformation on the PA registers, and the , that restricts the PA by forcing any two transitions on the same letter to affect the registers...
On the structure of multipliers of .
Affine Parikh automata
The Parikh finite word automaton (PA) was introduced and studied in 2003 by Klaedtke and Rueß. Natural variants of the PA arise from viewing a PA equivalently as an automaton that keeps a count of its transitions and semilinearly constrains their numbers. Here we adopt this view and define the , that extends the PA by having each transition induce an affine transformation on the PA registers, and the , that restricts the PA by forcing any two transitions on...
On normal homogeneous Einstein manifolds
Varieties with polynomially many models, I
A characterization of locally finite congruence modular varieties with the number of at most k-generated models being bounded from above by a polynomial in k is given. These are exactly the varieties polynomially equivalent to the varieties of unitary modules over a finite ring of finite representation type.
On the number of finite algebraic structures
We prove that every clone of operations on a finite set , if it contains a Malcev operation, is finitely related – i.e., identical with the clone of all operations respecting for some finitary relation over . It follows that for a fixed finite set , the set of all such Malcev clones is countable. This completes the solution of a problem that was first formulated in 1980, or earlier: how many Malcev clones can finite sets support? More generally, we prove that every finite algebra with few...
Affine Parikh automata
The Parikh finite word automaton (PA) was introduced and studied in 2003 by Klaedtke and Rueß. Natural variants of the PA arise from viewing a PA equivalently as an automaton that keeps a count of its transitions and semilinearly constrains their numbers. Here we adopt this view and define the , that extends the PA by having each transition induce an affine transformation on the PA registers, and the , that restricts the PA by forcing any two transitions on...
Quasiequational theories of flat algebras
We prove that finite flat digraph algebras and, more generally, finite compatible flat algebras satisfying a certain condition are finitely -based (possess a finite basis for their quasiequations). We also exhibit an example of a twelve-element compatible flat algebra that is not finitely -based.
The weak extension property and finite axiomatizability for quasivarieties
We define and compare a selection of congruence properties of quasivarieties, including the relative congruence meet semi-distributivity, RSD(∧), and the weak extension property, WEP. We prove that if 𝒦 ⊆ ℒ ⊆ ℒ' are quasivarieties of finite signature, and ℒ' is finitely generated while 𝒦 ⊨ WEP, then 𝒦 is finitely axiomatizable relative to ℒ. We prove for any quasivariety 𝒦 that 𝒦 ⊨ RSD(∧) iff 𝒦 has pseudo-complemented congruence lattices and 𝒦 ⊨ WEP. Applying these results and other results...
The variety generated by tournaments
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