We present constructions of countable two-dimensional subshifts of finite type (SFTs) with interesting properties. Our main focus is on properties of the topological derivatives and subpattern posets of these objects. We present a countable SFT whose iterated derivatives are maximally complex from the computational point of view, constructions of countable SFTs with high CantorBendixson ranks, ...

In the theory of generalized metric spaces, the notion of knetworks has played an important role. Every locally separable metric space or CW-complex, more generally, every space dominated by locally separable metric spaces has a star-countable k-network. Every LaSnev space, as well as, every space dominated by LaSnev spaces has a a-compact-finite knetwork. We recall that every space has a compa...

In this paper, the notions of countable S∗-compactness is introduced in L-topological spaces based on the notion of S∗-compactness. An S∗-compact L-set is countably S∗-compact. If L = [0, 1], then countable strong compactness implies countable S∗-compactness and countable S∗-compactness implies countable F-compactness, but each inverse is not true. The intersection of a countably S∗-compact L-s...

We investigate the relation between intermediate predicate logics based on countable linear Kripke frames with constant domains and Gödel logics. We show that for any such Kripke frame there is a Gödel logic which coincides with the logic defined by this Kripke frame on constant domains and vice versa. This allows us to transfer several recent results on Gödel logics to logics based on countabl...

We study separable metric spaces with few types of countable dense sets. We present a structure theorem for locally compact spaces having precisely n types of countable dense sets: such a space contains a subset S of size at most n−1 such that S is invariant under all homeomorphisms of X and X \ S is countable dense homogeneous. We prove that every Borel space having fewer than c types of count...

The G0-dichotomy due to Kechris, Solecki and Todorčević characterizes the analytic relations having a Borel-measurable countable coloring. We give a version of the G0-dichotomy for Σ 0 ξ-measurable countable colorings when ξ ≤ 3. A Σ 0 ξ-measurable countable coloring gives a covering of the diagonal consisting of countably many Σξ squares. This leads to the study of countable unions of Σξ recta...

Properties similar to countable fan-tightness are introduced and compared to countable tightness and countable fan-tightness. These properties are also investigated with respect to function spaces and certain classes of continuous mappings.

The minimal prime decomposition for semiprime ideals is defined and studied on z-ideals of C(X). The necessary and sufficient condition for existence of the minimal prime decomposition of a z-ideal / is given, when / satisfies one of the following conditions: (i) / is an intersection of maximal ideals. (ii) I is an intersection of O , s, when X is basically disconnected. (iii) I=O , when x X h...

We produce two separate algebraic descriptions of the isomorphism classes of the solvable subgroups of the group PLo(I) of piecewise-linear orientation-preserving homeomorphisms of the unit interval under the operation of composition, and also of the generalized R. Thompson groups Fn. The first description is as a set of isomorphism classes of groups which is closed under three algebraic operat...

We present results for pseudodifferential operators on Rd whose symbol a(·,ξ) is almost periodic (a.p.) for each ξ ∈ Rd and belongs to a Hörmander class Sm ρ,δ. We study a linear transformation a 7→ U(a) from a symbol a(x,ξ) to a frequency-dependent matrix U(a)(ξ)λ,λ′ , indexed by (λ,λ′) ∈ Λ×Λ where Λ is a countable set in Rd . The map a 7→ U(a) transforms symbols of a.p. pseudodifferential ope...