Related papers: Hereditary G-compactness

The aim of this paper is to continue the study of sg-compact spaces, a topological notion much stronger than hereditary compactness. We investigate the relations between sg-compact and $C_2$-spaces and the interrelations to hereditarily…

Let K be an algebraically bounded structure and T be its theory. If T is model complete, then the theory of K endowed with a derivation, denoted by $T^{\delta}$, has a model completion. Additionally, we prove that if the theory T is…

In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…

Godel's First Incompleteness Theorem is generalized to definable theories, which are not necessarily recursively enumerable, by using a couple of syntactic-semantic notions, one is the consistency of a theory with the set of all true…

A theory $T$ is said to have exact saturation at a singular cardinal $\kappa$ if it has a $\kappa$-saturated model which is not $\kappa^{+}$-saturated. We show, under some set-theoretic assumptions, that any simple theory has exact…

A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to…

We consider the random graph M^n_{\bar{p}} on the set [n], were the probability of {x,y} being an edge is p_{|x-y|}, and \bar{p}=(p_1,p_2,p_3,...) is a series of probabilities. We consider the set of all \bar{q} derived from \bar{p} by…

We prove structural theorems for computing the completion of a G-spectrum at the augmentation ideal of the Burnside ring of a finite group G. First we show that a G-spectrum can be replaced by a spectrum obtained by allowing only isotropy…

A group $G$ is invariably generated (IG) if there is a subset $S \subseteq G$ such that for every subset $S' \subseteq G$, obtained from $S$ by replacing each element with a conjugate, $S'$ generates $G$. $G$ is finitely invariably…

A topological space $X$ is called hereditarily supercompact if each closed subspace of X is supercompact. By a combined result of Bula, Nikiel, Tuncali, Tymchatyn, and Rudin, each monotonically normal compact Hausdorff space is hereditarily…

Assume $G$ is a solvable group whose elementary abelian sections are all finite. Suppose, further, that $p$ is a prime such that $G$ fails to contain any subgroups isomorphic to $C_{p^\infty}$. We show that if $G$ is nilpotent, then the…

Given a commutative ring $R$ and finitely generated ideal $I$, one can consider the classes of $I$-adically complete, $L_0^I$-complete and derived $I$-complete complexes. Under a mild assumption on the ideal $I$ called weak pro-regularity,…

We prove that for any monotone class of finite relational structures, the first-order theory of the class is NIP in the sense of stability theory if, and only if, the collection of Gaifman graphs of structures in this class is nowhere…

A profinite group G is just infinite if every non-trivial closed normal subgroup of G is of finite index, and hereditarily just infinite if every open subgroup is just infinite. Hereditarily just infinite profinite groups need not be…

A well-known theorem of P. Hall, usually called Hall's criterion for nilpotence, states: a group G is nilpotent whenever it has a normal subgroup N such that G/[N,N] and N are nilpotent. We widely generalize this result, replacing groups…

We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization…

Let $H$ be a subgroup of a group $G$. $H$ is said satisfying $\Pi$-property in $G$, if $|G/K:N_{G/K}(HK/K\cap L/K)|$ is a $\pi(HK/K\cap L/K))$-number for any chief factor $L/K$ of $G$, and, if there is a subnormal supplement $T$ of $H$ in…

In this note we show that a $p$-complete nilpotent space $X$ has a $p$-complete suspension spectrum if and only if its homotopy groups $\pi_*X$ are bounded $p$-torsion. In contrast, if $\pi_*X$ is not all bounded $p$-torsion, we locate…

A poset P is called reversible if every order preserving bijective self map of P is an order automorphism. P is called hereditarily reversible if every subposet of P is reversible. We give a complete characterization of hereditarily…

It is well known that whenever a class of structures $\mathcal{K}_1$ is interpretable in a class of structures $\mathcal{K}_2$, then the hereditary undecidability of (a fragment of) the theory of $\mathcal{K}_1$ implies the hereditary…