Questions on generalised Baire spaces

When studying questions about real numbers, it is common practice in set theory to investigate the closely related Baire space ω and Cantor space 2 . These spaces have been extensively studied by set theorists from various points of view, e.g., questions about cardinal characteristics of the continuum, descriptive set theory and other combinatorial questions. Furthermore, the investigation of 2 and ω has played a role in model theory, since countable structures can be coded as elements in these spaces (e.g., Scott’s and Lopez-Escobar’s theorems). Various motivations from the above areas have led to an interest among set theorists to study the uncountable analogues 2 and κ. In recent years, this subject has developed in its own right, with internally motivated open questions and a rich overarching theory. Moreover, unexpected applications to other areas of set theory and mathematics have been discovered (e.g., connections to large cardinals and forcing axioms).