The finite representation property for some reducts of relation algebras

Gautama代数和Almost Gautama代数的子簇中的融合性质

Amalgamation Property in the subvarieties of Gautama and Almost Gautama algebras

本文研究Almost Gautama代数簇的子簇中的融合性质，证明八个非平凡子簇中仅四个具有融合性质，并探讨了相关性质的应用。

The class of infinite dimensional quasipolaydic equality algebras is not finitely axiomatizable over its diagonal free reducts

We show that the class of infinite dimensional quasipolaydic equality algebras is not finitely axiomatizable over its diagonal free reducts

Factor Congruence Lifting Property

In previous work, we have introduced and studied a lifting property in congruence--distributive universal algebras which we have defined based on the Boolean congruences of such algebras, and which we have called the Congruence Boolean Lifting Property. In a similar way, a lifting property based on factor congruences can be defined in congruence--distributive algebras; in this paper we introduce this property, which we have called the Factor Congruence Lifting Property, and study it, partly in relation to the Congruence Boolean Lifting Property, and to other lifting properties in particular cl…

The small index property of the Fraïssé limit of finite Heyting algebras

We show that if a subgroup of the automorphism group of the Fraisse limit of finite Heyting algebras has a countable index, then it lies between the pointwise and setwise stabilizer of some finite set.

Finite Representation Property for Relation Algebra Reducts

The decision problem of membership in the Representation Class of Relation Algebras (RRA) for finite structures is undecidable. However, this does not hold for many Relation Algebra reduct languages. Two well known properties that are sufficient for decidability are the Finite Axiomatisability (FA) of the representation class and the Finite Representation Property (FRP). Furthermore, neither of the properties is stronger that the other, and thus, neither is also a necessary condition. Although many results are known in the area of FA, the FRP remains unknown for the majority of the reduct lang…

Algebraic geometry over algebraic structures III: Equationally Noetherian property and compactness

In this paper we discuss some special generalizations of equationally Noetherian property which naturally arise in the universal algebraic geometry. We introduce weakly equationally Noetherian, qw-compact, uw-compact, and weakly uw-compact algebras and then examine properties of such algebras. Also we consider the connections between five classes: the class of equationally Noetherian algebras, the class of weakly equationally Noetherian algebras, the class of uw-compact algebras, the class of weakly uw-compact algebras, and the class of qw-compact algebras.

On reduction and separation of projective sets in Tychonoff spaces

We show that for every Tychonoff space $X$ and Hausdorff operation $\mathbfΦ$, the class $\mathbfΦ(\mathscr Z,X)$ generated from zero sets in $X$ by $\mathbfΦ$ has the reduction or separation property if the corresponding class $\mathbfΦ(\mathscr F,\mathbb R)$ of sets of reals has the same property. In particular, under Projective Determinacy, these properties of such projective sets in $X$ have the same pattern as the First Periodicity Theorem states for projective sets of reals: the classes $\mathbfΣ^{1}_{2n}(\mathscr Z,X)$ and $\mathbfΠ^{1}_{2n+1}(\mathscr Z,X)$ have the reduction property …

Minimally generated Boolean algebras and the Nikodym property

A Boolean algebra $\mathcal A$ has the Nikodym property if every pointwise bounded sequence of bounded finitely additive measures on $\mathcal A$ is uniformly bounded. Assuming the Diamond Principle $\Diamond$, we will construct an example of a minimally generated Boolean algebra $\mathcal A$ with the Nikodym property. The Stone space of such an algebra must necessarily be an Efimov space. The converse is, however, not true - again under $\Diamond$ we will provide an example of a minimally generated Boolean algebra whose Stone space is Efimov but which does not have the Nikodym property. The r…