Related papers: Nicely generated and chaotic ideals

In [BKS15] examples of incomplete sentences are given with maximal models in more than one cardinality. The question was raised whether one can find similar examples of complete sentences. In this paper we give examples of complete…

Let $\kappa$ be any regular cardinal. Assuming the existence of a huge cardinal above $\kappa$, we prove the consistency of $\binom{\kappa^{++}}{\kappa^+}\rightarrow\binom{\tau}{\kappa^+}$ for every ordinal $\tau<\kappa^{++}$. Likewise, we…

Jech proved that every partially ordered set can be embedded into the cardinals of some model of $ZF$. We extend this result to show that every partially ordered set can be embedded into the cardinals of some model of $ZF+DC_{<\kappa}$ for…

We use the core model for sequences of measures to prove a new lower bound for the consistency strength of the failure of the SCH: THEOREM (i) If there is a singular strong limit cardinal $\kappa$ such that $2^\kappa > kappa^+$ then there…

We use a natural forcing to construct a left-separated topology on an arbitrary cardinal kappa. The resulting left-separated space X_kappa is also 0-dimensional T_2, hereditarily Lindelof, and countably tight. Moreover if kappa is regular…

We show that every null-additive set is meager-additive, where: (1) a set X subseteq 2^omega is null-additive if for every Lebesgue null set A subseteq 2^omega, X+A is null too; (2) we say that X subseteq 2^omega is meager-additive if for…

It is known that a Banach space contains an isomorphic copy of $c_0$ if, and only if, it can be equivalently renormed to be almost square. We introduce and study transfinite versions of almost square Banach spaces with the purpose to relate…

In this note we consider an arbitrary families of sets of $s_0$ ideal introduced by Marczewski-Szpilrajn. We show that in any uncountable Polish space $X$ and under some combinatorial and set theoretical assumptions ($cov(s_0)=\c$ for…

A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure has a…

Abstractly, the generic extensions after $\aleph_\omega$-many Cohen reals and $\aleph_{\omega+1}$-many Cohen reals must be different for reasons of uniform density the relevant Boolean algebras. Nevertheless this is not satisfying and it…

Building on work of Holy, L\"ucke and Njegomir \cite{MR3913154} on small embedding characterizations of large cardinals, we use some classical results of Baumgartner (see \cite{MR0384553} and \cite{MR0540770}), to give characterizations of…

We give a new proof of a theorem of Becker that under AD+V=L(R), omega_2 is a kappa-supercompact for every kappa less than or equal to the supremum of all Suslin cardinals. Our proof uses inner model theory. It is still open whether one can…

We point out some connections between existence of homogenous sets for certain edge colorings and existence of branches in certain trees. As a consequence, we get that any locally additive coloring (a notion introduced in the paper) of a…

We show that the number of types of sequences of tuples of a fixed length can be calculated from the number of 1-types and the length of the sequences. Specifically, if $\kappa \leq \lambda$, then $$\sup_{|A| = \lambda} |S^\kappa(A)| =…

Let 2<n\leq l<m< \omega. Let L_n denote first order logic restricted to the first n variables. We show that the omitting types theorem fails dramatically for the n--variable fragments of first order logic with respect to clique guarded…

Let $\big(\mathcal{S}_n^{\alpha,\kappa,\mathfrak{r}}(z)\big)_{n=1}^\infty$ be a sequence of the largest possible integer intervals, such that…

We show that an embedding of a fixed 0-dimensional compact space $K$ into the \v{C}ech--Stone remainder $\omega^*$ as a nowhere dense P-set is the unique generic limit, a special object in the category consisting of all continuous maps from…

Suppose that $X$ is a Banach space. We will show that $X$ does not contain a copy of $c_0$ if and only if for each series which is not unconditionally convergent in $X$ respective sets coding all bounded subseries and rearrangements are…

For a discrete group $G$, we use the natural correspondence between ideals in the Boolean algebra $ \mathcal{P}_G$ of subsets of $G$ and closed subsets in the Stone-$\check{C}$ech compactifi-cation $\beta G$ as a right topological semigroup…

We continue our study of Sierpinski-type colourings. In contrast to the prequel paper, we focus here on colourings for ideals stratified by their completeness degree. In particular, improving upon Ulam's theorem and its extension by Hajnal,…