Related papers: On the number of independent orders

We generalize the Hart-Shelah example \cite{HaSh:323} to higher infinitary logics. We build, for each natural number $k\geq 2$ and for each infinite cardinal $\lambda$, a sentence $\psi_k^\lambda$ of the logic $L_{(2^\lambda)^+,\omega}$…

We show that if \kappa\ is a weakly compact cardinal then the embeddability relation on (generalized) trees of size \kappa\ is invariantly universal. This means that for every analytic quasi-order R on the generalized Cantor space 2^\kappa\…

We investigate which classes of infinite graphs have the Erd\H{o}s-P\'osa property (EPP). In addition to the usual EPP, we also consider the following infinite variant of the EPP: a class $\mathcal{G}$ of graphs has the $\kappa$-EPP, where…

Let $\mathcal{S}$ be a commutative semigroup, and let $T$ be a sequence of terms from the semigroup $\mathcal{S}$. We call $T$ an (additively) {\sl irreducible} sequence provided that no sum of its some terms vanishes. Given any element $a$…

We discuss intrinsic aspects of Krupka's approach to finite-order variational sequences. We give intrinsic isomorphisms of the quotient subsheaves of the short finite-order variational sequence with sheaves of forms on jet spaces of…

In 1956, 48 years after Hausdorff provided a comprehensive account on ordered sets and defined the notion of a scattered order, Erd\H{o}s and Rado founded the partition calculus in a seminal paper. The present paper gives an account of…

Let $\mathsf{KP}$ denote Kripke-Platek Set Theory and let $\mathsf{M}$ be the weak set theory obtained from $\mathsf{ZF}$ by removing the collection scheme, restricting separation to $\Delta_0$-formulae and adding an axiom asserting that…

The ultrapower theorem of Keisler-Shelah allows such model-theoretic notions as elementary equivalence, elementary embedding and existential embedding to be couched in the language of categories (limits, morphism diagrams). This in turn…

We point out a gap in Shelah's proof of the following result: $\mathbf{Claim}$ Let $K$ be an abstract elementary class categorical in unboundedly many cardinals. Then there exists a cardinal $\lambda$ such that whenever $M, N \in K$ have…

Shelah shows that certain revised countable support (RCS) iterations do not add reals. His motivation is to establish the independence (relative to large cardinals) of Avraham's problem on the existence of uncountable non-constuctible…

We consider topological insulators and superconductors with discrete symmetries and clarify the relevant index theory behind the periodic table proposed by Kitaev. An effective Hamiltonian determines the analytical index, which can be…

For $\mu, \kappa$ infinite, say $\mathcal{A}\subseteq [\kappa]^\kappa$ is a $(\mu,\kappa)$-maximal independent family if whenever $\mathcal{A}_0$ and $\mathcal{A}_1$ are pairwise disjoint non-empty in $[\mathcal{A}]^{<\mu}$ then…

This paper is a contribution to Vinberg's theory of $\theta$-groups, or in other words, to Invariant Theory of periodically graded semisimple Lie algebras. One of our main tools is Springer's theory of regular elements of finite reflection…

Let $\mathfrak{i}$ denote the minimal cardinality of a maximal independent family and let $\mathfrak{a}_T$ denote the minimal cardinality of a maximal family of pairwise almost disjoint subtrees of $2^{<\omega}$. Using a countable support…

For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties. We also study their limits when the…

Let K be an Abstract Elemenetary Class satisfying the amalgamation and the joint embedding property, let \mu be the Hanf number of K. Suppose K is tame. MAIN COROLLARY: (ZFC) If K is categorical in a successor cardinal bigger than…

We show that if the universe is self-iterable and $\kappa$ is an inaccessible limit of Woodin cardinal then $AD_R + "\Theta$ is regular" holds in the derived model at $\kappa$. The proof is fine-structure free, and only assumes basic…

Dissipative systems play a very important role in several physical models, most notably in Celestial Mechanics, where the dissipation drives the motion of natural and artificial satellites, leading them to migration of orbits, resonant…

Let H be a pseudovariety of groups in which the kappa-word problem is decidable. Here, kappa denotes the canonical implicit signature, which consists of the multiplication and the (omega-1)-power. We prove that the kappa-word problem is…

We study the $\kappa$-Borel-reducibility of isomorphism relations of complete first order theories by using coloured trees. Under some cardinality assumptions, we show the following: For all theories T and T', if T is classifiable and T' is…