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Let X be a non-empty set. By O(X) we denote the set of all finitary operations on X, i.e. all functions X → X of arbitrary arity n. A clone on X is a subset of O(X) which contains all projections, i.e. all mappings (x1, . . . , xn) 7→ xi for arbitrary 1 ≤ i ≤ n, and which is closed under superposition, i.e. together with f : X → X and g1, . . . , gn : X m →… (More)

On an infinite base set X, every ideal of subsets of X can be associated with the clone of those operations on X which map small sets to small sets. We continue earlier investigations on the position of such clones in the clone lattice.

- Lutz Heindorf
- Math. Log. Q.
- 1981

We investigate the near-unanimity problem: given a finite algebra, decide if it has a near-unanimity term of finite arity. We prove that it is undecidable of a finite algebra if it has a partial near-unanimity term on its underlying set excluding two fixed elements. On the other hand, based on Rosenberg’s characterization of maximal clones, we present… (More)

Let X denote an arbitrary second-countable, compact, zero-dimensional space. Our main result says that A' is a graph space, i.e., homeomorphic to the space of all complete subgraphs of a suitable graph. We first characterize graph spaces in terms of the Boolean algebras of their clopen subsets. Then it is proved that each countable Boolean algebra has the… (More)

- Lutz Heindorf
- Math. Log. Q.
- 1984

- Lutz Heindorf
- 2010

We prove what the title says. It then follows that zero-dimensional Dugundji space are supercompact. Moreover, their Boolean algebras of clopen subsets turn out to be semigroup algebras.

- Lutz Heindorf
- 1995

Throughout this paper X denotes a compact and zero-dimensional Hausdorr space. We shall be concerned with Theorem 0.1 The following assertions are equivalent. (A) X is the continuous image of a compact ordered space. (B) X is the continuous image of a zero-dimensional compact ordered space. (C) X has a T 0-separating cross-free family of clopen sets. (D) X… (More)

- Lutz Heindorf
- 2010

We prove that a Boolean algebra is countable iff its subalgebra lattice admits a continuous complementation.

- Lutz Heindorf
- Easter Conference on Model Theory
- 1989