Related papers: Ladders and Squares

A space X is kappa-resolvable (resp. almost kappa-resolvable) if it contains kappa dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets of X). Answering a problem raised by Juhasz, Soukup, and…

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…

In this paper we investigate more characterizations and applications of $\delta$-strongly compact cardinals. We show that, for a cardinal $\kappa$ the following are equivalent: (1) $\kappa$ is $\delta$-strongly compact, (2) For every…

Two graphs are of the same topological type if they can be mutually embedded into each other topologically. We show that there are exactly $\aleph_1$ distinct topological types of countable trees. In general, for any infinite cardinal…

We study the smallest, as well as the largest numbers of congruences of lattices of an arbitrary finite cardinality $n$. Continuing the work of Freese and Cz\' edli, we prove that the third, fourth and fifth largest numbers of congruences…

An inaccessible cardinal $\kappa$ is supercompact when $(\kappa, \lambda)$-ITP holds for all $\lambda\geq \kappa.$ We prove that if there is a model of $\ZFC$ with two supercompact cardinals, then there is a model of \ZFC where…

Let $\kappa$ be an inaccessible cardinal, $\mathfrak{U}$ be a universal algebra, and $\sim$ be the equivalence relation on $\mathfrak{U}^{\kappa}$ of eventual equality. From mild assumptions on $\kappa$ we give general constructions of…

We discuss some well-known compactness principles for uncountable structures of small regular sizes ($\omega_n$ for $2 \le n<\omega$, $\aleph_{\omega+1}$, $\aleph_{\omega^2+1}$, etc.), consistent from weakly compact (the size-restricted…

For each cardinal $\kappa$, each natural number $n$ and each simplicial complex $K$ we construct a space $\nu^n_\kappa(K)$ and a map $\pi \colon \nu^n_\kappa(K) \to K$ such that the following conditions are satisfied. 1. $\nu^n_\kappa(K)$…

It is a long discussed issue whether light scalar mesons have sizeable four-quark components. We present an exploratory study of this question using N_f=2+1+1 twisted mass lattice QCD. A mixed action approach ignoring disconnected…

We introduce a new compactness principle which we call the gluing property. For a measurable cardinal $\kappa$ and a cardinal $\lambda$, we say that $\kappa$ has the $\lambda$-gluing property if every sequence of $\lambda$-many…

One of the numerous characterizations of a Ramsey cardinal kappa involves the existence of certain types of elementary embeddings for transitive sets of size \kappa satisfying a large fragment of ZFC. We introduce new large cardinal axioms…

The purpose of this article is to give new constructions of linear orders which are minimal with respect to being non-$\sigma$-scattered. Specifically, we will show that Jensen's principle $\diamondsuit$ implies that there is a minimal…

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…

If L is an order polynomially complete lattice, (that is: every monotone function from L^n to L is induced by a lattice-theoretic polynomial) then the cardinality of L is a strongly inaccessible cardinal. In particular, the existence of…

The Kalikow problem for a pair (lambda, kappa) of cardinal numbers, lambda > kappa (in particular kappa =2) is whether we can map the family of omega --sequences from lambda to the family of omega --sequences from kappa in a very continuous…

We deal with (< kappa)-supported iterated forcing notions which are (E_0,E_1)-complete, have in mind problems on Whitehead groups, uniformizations and the general problem. We deal mainly with the successor of a singular case. This continues…

Let $\mathrm{cof}(\mu)=\mu$ and $\kappa$ be a supercompact cardinal with $\mu<\kappa$. Assume that there is an increasing and continuous sequence of cardinals $\langle\kappa_\xi\mid \xi<\mu\rangle$ with $\kappa_0:=\kappa$ and such that, for…

Assuming 0^sharp does not exist, kappa is an uncountable cardinal and for all cardinals lambda with kappa <= lambda < kappa^{+ omega}, 2^lambda = lambda^+, we present a ``mini-coding'' between kappa and kappa^{+ omega}. This allows us to…

Given a weakly compact cardinal $\kappa$, we give an axiomatization of intuitionistic first-order logic over $\mathcal{L}_{\kappa^+, \kappa}$ and prove it is sound and complete with respect to Kripke models. As a consequence we get the…