If A and B are subsets of an abelian group, their sumset is $A+B:=\{a+b:a\in A, b\in B\}$. We study sumsets in discrete abelian groups, where at least one summand has positive upper Banach density.

Jin proved in [27] that if A and B are sets of integers having positive upper Banach density, then $A+B$ is piecewise syndetic. Bergelson, Furstenberg, and Weiss [4] improved the conclusion to “$A+B$ is piecewise Bohr.” In [2] this was shown to be qualitatively optimal, in the sense that if $C\subseteq \mathbb Z$ is piecewise Bohr, then there are $A, B\subseteq \mathbb Z$ having positive upper Banach density such that $A+B\subseteq C$.

We improve these results by establishing a strong correspondence between sumsets in discrete abelian groups, level sets of convolutions in compact abelian groups, and sumsets in compact abelian groups. Our proofs avoid measure preserving dynamics and nonstandard analysis, and our results apply to discrete abelian groups of any cardinality.

How does technological change affect social policy preferences? We advance this lively debate by focusing on the role of dual vocational education and training (VET). Existing literature would lead us to expect that dual VET increases demand for compensatory social policy and magnifies the effect of automation risk on such demands. In contrast, we contend that dual VET weakens demand for compensatory social policy through three non-mutually exclusive mechanisms that we refer to as (i) material self-interest; (ii) workplace socialization; and (iii) skill certification. We further hypothesize that dual VET mitigates the association between automation risk and social policy preferences. Analyzing cross-national individual data from the European Social Survey and national-level data on education systems, we find strong evidence for our argument. The paper advances the debate on social policy preferences in the age of automation and sheds new light on the relationship between skill formation and social policy preferences.

The roots of the concept of human dignity have habitually been traced back to Immanuel Kant. However, recent scholarship suggests that this might be a false parentage, and feminist theorists have long criticized the gendered nature of Kantian dignity. This paper suggests looking to another thinker for the origins of human dignity: Mary Wollstonecraft. Wollstonecraft’s notion of dignity more closely resembles present currents of thought about the concept and offers a sterner defence of moral equality for women as well as men. To demonstrate this, the paper first analyses what Wollstonecraft understood by the term “dignity,” and then explores the wider role that it played in her thought, and especially her analysis of the French Revolution.

The Agreement between the Council of Europe and Ukraine establishes a Special Tribunal to prosecute individuals bearing the greatest responsibility for the crime of aggression against Ukraine. Adopted in June 2025, the treaty-based tribunal responds to Russia’s use of force beginning in 2014 and escalating in 2022. The Tribunal’s Statute explicitly removes head of state immunity, ensuring that senior leaders may face prosecution. Jurisdiction is limited to aggression as defined by UN General Assembly Resolution 3314. The institutional framework includes chambers, a prosecutor’s office, and a registry, with robust fair trial guarantees. This represents a significant development in international criminal justice and accountability for leadership crimes.

This study presents a corpus-based analysis of the verb blîven in combination with the present participle and the infinitive in Middle Low German (thirteenth–seventeenth century), with the goal of identifying the aspectual and semantic properties of these constructions. In contrast to previous research, which focused primarily on the verbs wērden and wēsen or relied on limited textual material, the present study draws on a broader corpus, allowing for a more comprehensive assessment of usage patterns across different periods and genres.

The analysis shows that blîven in combination with a present participle or an infinitive can express both mutative and nonmutative meanings, with the nonmutative interpretation clearly predominating regardless of form. The study further explores how the aspectual interaction between blîven and the nonfinite verb influences the overall interpretation of the construction.

The semantic patterns observed for blîven are compared with those found in wērden and wēsen + present participle constructions, revealing significant semantic convergence among Middle Low German predicative structures. These findings contribute to a deeper understanding of the development and aspectual behavior of periphrastic constructions in the historical Germanic languages.*

The current study examines the effect of talker identity and linguistic experience on the perception of novel speech patterns by English speakers, focusing on vowel insertion in Korean-accented English. Experiment 1 shows that English speakers with no experience of living in Korea identify English words with vowel insertion as valid words more frequently throughout the experiment only when the talker is described as Korean, but not when the talker is American or Mexican. In Experiment 2, we find similar results with English speakers living in Korea, who provide more word responses to vowel-inserted English words in the Korean talker condition but not the American talker condition. Comparing Experiment 1 and Experiment 2, participants living in Korea show a greater preference for the inserted vowel that is similar to the one found in Korean-accented English ([ʊ]) over the control vowel ([ɪ]), as well as faster adaptation to this type. These results suggest that both talker identity and previous exposure to an accent influence how listeners perceive and adapt to foreign-accented speech, consistent with exemplar models of speech perception.