Let M be a compact smooth manifold without boundary. Based on results by Good and Meddaugh [Invent. Math. 220 (2020), 715–736], we prove that a strong distributional chaos is $C^0$ -generic in the space of continuous self-maps (respectively, homeomorphisms) of M. The results contain answers to questions by Li, Li and Tu [Chaos 26 (2016), 093103] and Moothathu [Topology Appl. 158 (2011), 2232–2239] in the zero-dimensional case. A related counter-example on the chain components under shadowing is also given.

In this paper we show that generic continuous Lebesgue measure-preserving circle maps have the s-limit shadowing property. In addition, we obtain that s-limit shadowing is a generic property also for continuous circle maps. In particular, this implies that classical shadowing, periodic shadowing and limit shadowing are generic in these two settings as well.

A set $G \subseteq \omega$ is n-generic for a positive integer n if and only if every ${\rm{\Sigma }}_n^0$ formula of G is decided by a finite initial segment of G in the sense of Cohen forcing. It is shown here that every n-generic set G is properly ${\rm{\Sigma }}_n^0$ in some G-recursive X. As a corollary, we also prove that for every $n > 1$ and every n-generic set G there exists a G-recursive X which is generalized ${\rm{lo}}{{\rm{w}}_n}$ but not generalized ${\rm{lo}}{{\rm{w}}_{n - 1}}$. Thus we confirm two conjectures of Jockusch [4].

“Simple generics” with bare plural subjects (e.g., dogs bark) predicate of a kind a property that the kind “inherits” from its individual members. But what does that inheritance amount to if it is not, like most dogs bark, based on how many individuals have the property. My conclusion: there is no determinate account of which (fundamentally individual-level) properties can be truly predicated of a kind: generics are not quantificational, and language users’ interests guide judgments on their truth-conditions. At the same time, even “canonical” predications of ordinary predicates of ordinary individuals are not so straightforward as they might appear. Generic claims about social groups show the indeterminacy of truth conditions for simple generics and the relation to stereotypes and sometimes conflicting interests.

I argue in favor of a distinctive generic form of essence and ground and show how the two notions thereby complement one another as forms of necessary and sufficient condition.

The problems of poor or biased information and of misleading health and well-being advice on the Internet have been extensively documented. The recent decision by the Internet Corporation for Assigned Names and Numbers to authorize a large number of new generic, top-level domains, including some with a clear connection to health or healthcare, presents an opportunity to bring some order to this chaotic situation. In the case of the most general of these domains, “.health,” experts advance a compelling argument in favor of some degree of content oversight and control. On the opposing side, advocates for an unrestricted and open Internet counter that this taken-for-granted principle is too valuable to be compromised, and that, once lost, it may never be recovered. We advance and provide evidence for a proposal to bridge the credibility gap in online health information by providing provenance information for websites in the .health domain.

We study model-theoretic and stability-theoretic properties of the non-abelian free group in the light of Sela's recent result on stability and results announced by Bestvina and Feighn on ‘negligible subsets' of free groups. We point out analogies between the free group and so-called bad groups of finite Morley rank, and prove ‘non-CM-triviality' of the free group.

We define a notion of genericity for arbitrary subgroups of groups interpretable in a simple theory, and show that a type generic for such a group is generic for the minimal hyperdefinable supergroup (the definable hull). In particular, at least one generic type of the definable hull is finitely satisfiable in the original subgroup. If the subgroup is a subfield. then the additive and the multiplicative definable hull both have bounded index in the smallest hyperdefinable superfield.

Differentiability properties of optimal value functions associated with perturbed optimization problems require strong assumptions. We consider such a set of assumptions which does not use compactness hypothesis but which involves a kind of coherence property. Moreover, a strict differentiability property is obtained by using techniques of Ekeland and Lebourg and a result of Preiss. Such a strengthening is required in order to obtain genericity results.

We investigate categorical and amalgamation properties of the functor $\operatorname{Id_c}$ assigning to every partially ordered abelian group $G$ its $\langle \vee, 0 \rangle$-semilattice of compact ideals $\operatorname{Id_c} G$. Our main result is the following.

Theorem 1. Every diagram of finite Boolean semilattices indexed by a finite dismantlable partially ordered set can be lifted, with respect to the$\operatorname{Id_c}$functor, by a diagram of pseudo-simplicial vector spaces.

Pseudo-simplicial vector spaces are a special kind of finite-dimensional partially ordered vector spaces with interpolation over the field of rational numbers. The methods introduced also make it possible to prove the following ring-theoretical result.

Theorem 2. For any countable distributive$\langle \vee, 0 \rangle$-semilattices$S$and$T$and any field$K$, any$\langle \vee, 0 \rangle$-homomorphism$f \colon S \to T$can be lifted, with respect to the$\operatorname{Id_c}$functor on rings, by a homomorphism $f \colon A \to B$of$K$-algebras, for countably dimensional locally matricial algebras$A$and$B$over$K$.

We also state a lattice-theoretical analogue of Theorem 2 (with respect to the $\operatorname{Con_c}$ functor), and we provide counterexamples to various related statements. In particular, we prove that the result of Theorem 1 cannot be achieved with simplicial vector spaces alone.

This study examines the types of interactional trouble that arise from narrative variation in institutional interviews. Specifically, we examine protective order interviews in which Latina women tell of domestic violence to paralegal interviewers charged with the duty of helping them obtain a protective order. Victims' narratives are shown to take different shapes, and paralegals respond to them in different pragmalinguistic ways, depending on how they diverge from institutional needs. The factors found most heavily to influence narrative outcomes are contextual ones, related to participant social roles, the type of communicative activity interlocutors perceive themselves to be engaged in, and their interactional goals. An additional finding is that when expectations of what constitutes appropriate speech behavior differ, the interlocutor holding greater institutional power will try to constrain the speech of the other, despite the fact that both appear to share an extralinguistic goal, in this case obtaining a protective order.