Motivated by ideas from the study of abstract data types, we show how to interpret non-well-founded sets as tixed points of continuous transformations of an initial continuous algebra. We conisder a preordered structure closely related to the set HF of well-founded, hereditarily finite sets. By taking its ideal completion, we obtain an initial continuous algebra in which we are able to solve al...

The co-elementary hierarchy is a nested ordinal-indexed sequence of classes of mappings between compacta, with each successor level being defined inductively from the previous one using the topological ultracopower construction. The lowest level is the class of continuous surjections; and the next level up, the coexistential maps, is already a much more restricted class. Co-existential maps are...

The co-elementary hierarchy is a nested ordinalindexed sequence of classes of mappings between compacta, with each successor level being defined inductively from the previous one using the topological ultracopower construction. The lowest level is the class of continuous surjections; and the next level up, the co-existential maps, is already a much more restricted class. Co-existential maps are...

For a hereditarily unicoherent continuum X, its kernel means the common part of all subcontinua of X that intersect all arc components of X. This concept naturally appears when absolute retracts for the class of hereditarily unicoherent continua are studied. Let Y be such an absolute retract. Among other results, we prove that (a) Y is indecomposable if and only if it is identical with its kern...

In this paper we prove that Japaridze’s Polymodal Logic is PSPACE-decidable. To show this, we describe a decision procedure for satisfiability on hereditarily ordered frames that can be applied to obtain upper complexity bounds for various modal logics.