This proposed research is in mathematical logic and foundations of mathematics, more specifically in set theory. It is motivated by the interplay between regularity properties and definability for subsets of real numbers. By "regularity properties" we are referring to certain desirable properties of sets, and by "definability" to the logical description of such sets, in the sense of Descriptive Set Theory. The study of such questions goes back to classical issues in topology, analysis and related fields of mathematics, raised by the great pioneers of abstract mathematics of the late 19th and early 20th century, such as Georg Cantor, Emile Borel, Henri Lebesgue and others. These mathematicians were faced with seemingly insurmountable challenges which could only be resolved later with the advent of logical and meta-mathematical methods, developed by Kurt Gödel in 1938 and by Paul Cohen in 1964. Since that time, the study of Regularity Properties has continued to hold a central position in the foundations of mathematics. Many mathematicians and logicians of high status and prestige have contributed to this area, among them W. Hugh Woodin (winner of the Hausdorff Medal 2013), Stevo Todorčević (winner of the CRM-Fields-PIMS prize 2012) and Saharon Shelah (winner of numerous awards, among them the Erdös Prize 1977 and the Karp Prize 1983). We propose to contribute to this line of research in a number of interrelated directions, such as: studying new regularity properties (relevant to other fields of mathematics), developing abstract frameworks for such properties, studying higher complexity classes, and generalising results to spaces other than the classical real numbers. Several technical results involving the method of "forcing" needed to construct models of set theory, will also be worked out along the way.

The COVID-19 pandemic has exposed our shared vulnerability to isolation, serving as a reminder that relations of marginalization and exclusion constitute significant obstacles to the achievement of a society in which everyone can fully participate and stand in relations of equality with each other. Moreover, empirical research has shown that marginalised individuals are being disproportionately disadvantaged by the Coronavirus emergency in several ways: they are the target of stigmatization and discrimination. And, although they are more likely to experience mental health issues and are typically exposed to serious health risks, they are not provided access to the same degree of medical care as other members of society. The current socio-political state of affairs, then, vividly illustrates how persons' vulnerability to social exclusion is one of the most pressing social justice challenges that liberal democracies must face. Building on my previous research on the justification and the value of equality, in this project I will contribute to the Horizon Europe strategic plan towards "creating a more resilient, inclusive and democratic European society" by developing the first-ever comprehensive liberal egalitarian theory of vulnerability to social exclusion in analytical political philosophy. This theory will define the rights that marginalized individuals have to be fully included as equals in society and identify the social arrangements that the state ought to put in place in order to ameliorate their social condition. In our current pluralist and diverse societies the call for social equality is ubiquitous but its precise meaning is contested. By providing an account of what shape equality takes when applied to socially marginalized groups, this research will thus fill an important theoretical and normative gap when thinking about what a just society owes to its most vulnerable members if they are to be considered and treated as equals.

Words in sign languages are rich in visual meaning. They contain shapes, movements, relations in space, etc. that depict objects and actions as symbolic metaphors; e.g., the action of pulling words out of the head in one language means ‘to ponder’. Yet, signs are also encoded into units of form that are articulated in simultaneous constructions, unlike sequences of consonants and vowels in spoken words. How, then, do signers store richly symbolic words that occur in highly simultaneous forms in their mental lexicons? At present, insight into these mental mappings remains highly occluded, not only at the level of behavioral and neural phenomena, but in terms of linguistic analysis as well. What, indeed, is morphology in sign languages when even the smallest units of form—like hooked fingers or a location at the throat—can carry meaning? What is the nature of these units? Do they vary across sign languages or are the iconic roots of form-meaning mappings so powerful that the same ones re-occur across unrelated sign languages? Answering these questions is urgently needed to create better sign language resources for teaching and learning, and to advance language technologies. The SemaSign project proposes a ground-breaking approach to these questions by locating form-meaning correspondences in sign languages through computational means while creating new empirically-robust datasets to reveal how signs are organized in the mental lexicon. Semantic networks are created for sign languages from Germany, Kenya, and Guinea Bissau on the basis of word association responses in which a signer sees a sign from their language and responds with the first three signs that come to mind. This will establish an objective measure of semantic relatedness, enabling computational means to locate clusters of signs unusually close in both form and meaning. As the language in Guinea Bissau was formed only 15 years ago, we will also discover how lexicons emerge and grow at a very early stage

SIHAFA explores the late Ottoman (1890s–1918) Arabic ideosphere of the Eastern Mediterranean through its periodical press. SIHAFA transcends the individual periodical for a systematic and computational study of the periodical press as a discursive field and at scale in order to better understand both the intellectual history of the Eastern Mediterranean at a crucial historical juncture and periodical production itself. As MSCA fellow, Dr. Grallert will receive crucial training at Universität Hamburg and will scrutinise a digital corpus of seven Arabic journals from Baghdad, Beirut, Cairo and Damascus with more than 7 million words (the result of his current research) through a combination of stylometric authorship attribution, social network analysis, and close reading of bio-bibliographical dictionaries. He will evaluate theoretical and methodological approaches, workflows, and tools developed in the Global North for their applicability to cultural heritage of the Global South. A secondment at Uniwersytet Jagielloński will provide methodological training in stylometry. The research objectives are to: (1) fill a gap in research by developing and evaluating methods for the study of Arabic periodicals; (2) challenge established narratives of the Arabic Renaissance (nahda) by re-introducing non-Syrian and Muslim authors and periodicals from beyond Cairo and Beirut commonly ignored by scholarly literature through the leading research question "What were the core nodes of authors and periodicals in this ideosphere and how did they change over time?"; (3) help establish the field of Arab Periodical Studies through community building across the postcolonial north-south divide. SIHAFA is committed to FAIR data and open access. Dr. Grallert will produce and publish: ground-breaking research to be published in English and Arabic; improved digital scholarly editions; authority files; an OCR model for Arabic periodicals; and a plain text corpus of authorship candidates.