More game-theoretic properties of boolean algebras

The following infinite game $\text{G}$ was investigated in [5]: Let B be a Boolean algebra. Two players, White and Black, take turns to choose successively a sequence     

Isomorphically rigid algebras

Various classes of non-associative algebras possessing the property of being rigid under abstract isomorphisms are studied. Supported by RFBR grant No. 06-01-00159a. __________ Translated from Algebra i Logika, Vol. 46, No. 4, pp. 483–502, July–August, 2007.     

The number of monounary algebras

In this note we give an asymptotic estimate for the number of finite non-isomorphic monounary algebras of a given size.     

Saturated boolean algebras and their stone spaces

For an infinite cardinal κ, we call a compact zero-dimensional space a κ-Parovicenko space if its boolean algebra of clopen sets is κ-saturated and has cardinality κ^<κ. We answer some questions about these spaces which were posed in [14]. For instance, it is shown that a κ⁺-Parovicenko spacé can be a Stone-Cech remainder in a natural way. We show that some of the results in [14] which used the assumption κ^<κ=κ, do indeed require this assumption. We also show that if 2^κ=κ⁺ then each compact F_κ⁺-space with weight κ⁺ can be embedded into a κ⁺-Parovicenko space (and so into an extremally disconnected space).