Related papers: A first-countable non-remainder of H
In this paper we continue our study, begun in part I, of the exceptional set of integers, not restricted by elementary congruence conditions, which cannot be represented as sums of three or four squares of primes. We correct a serious…
We give different proofs and prove new results on the non complete solvability of some systems of complex first order p.d.e.'s, especially related to the analysis on CR manifolds.
The uncountability of the reals was first established by Cantor in what was later heralded as the first paper on set theory. Since the latter constitutes the official foundations of mathematics, the logical study of the uncountability of…
We construct a non-separable C*-algebra that is prime but not primitive.
In this paper, we prove the number of countable models of a countable supersimple theory is either 1 or infinite. This result is an extension of Lachlan's theorem on a superstable theory.
The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one…
In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an 'essential' way. A common feature of such theories is that they do not interpret any infinite discrete…
We provide a countable series of bisimple $\mathcal{H}$-trivial finitely presented congruence-free monoids.
We give an elementary proof of a monotone selection principle which allows to pass from increasing nets to increasing sequences in the Hermitian part of a $\sigma$-finite von Neumann algebra. This is to be seen as a ``monotone version'' of…
This paper examines a denumerable version of the nested-set theorem and derives from it a contradiction involving the formal consistency of the actual infinity assumed by the Axiom of Infinity.
Schnorr showed that a real is Martin-Loef random if and only if all of its initial segments are incompressible with respect to prefix-free complexity. Fortnow and independently Nies, Stephan and Terwijn noticed that this statement remains…
We classify essential algebras whose irredundant non-refinable covers consist of primal algebras. The proof is obtained by constructing one to one correspondence between such algebras and partial orders on finite sets. Further, we prove…
Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…
In this article we obtain a complete description of the congruences of lines in $\p^4$ of order one provided that the fundamental surface $F$ is non-reduced (and possibly reducible) at one of its generic points, and their classification…
Answering a question of Junker and Ziegler, we construct a countable first order structure which is not omega-categorical, but does not have any proper non-trivial reducts, in either of two senses (model-theoretic, and group-theoretic). We…
We give examples of $n$-sequentially compact spaces that are not $(n+1)$-sequentially compact under several assumptions. We improve results from Kubis and Szeptycki by building such examples from $\mathfrak{b=c}$ and…
We construct a continuum of non-homeomorphic compact subspaces of the real line R without singleton components. Thus from the purely topological point of view the real line contains not only more closed sets than open sets but also more…
We study elements of second order linear recurrence sequences $(G_n)_{n= 0}^{\infty}$ of polynomials in $\mathbb{C}[x]$ which are decomposable, i.e. representable as $G_n=g\circ h$ for some $g, h\in \mathbb{C}[x]$ satisfying…
Denote by $\continuum=2^{\aleph_0}$ the cardinal of continuum. We construct an intriguing family $(P_\alpha: \alpha\in\continuum)$ of prime $z$-ideals in $\C_0(\reals)$ with the following properties: If $f\in P_{i_0}$ for some…
The first examples of formations which are arboreous (and therefore Hall) but not freely indexed (and therefore not locally extensible) are found. Likewise, the first examples of solvable formations which are freely indexed and arboreous…