Transfinite set theory encompasses the rigorous study of infinite hierarchies, particularly those structured by ordinals and cardinals. This field has been instrumental in deepening our comprehension ...

Set theory, the mathematical study of collections of objects, forms a foundation for much of modern mathematics, while cardinal functions provide a means to quantify the sizes of these sets, ...

Synthese, Vol. 192, No. 8, Special Section on HISTORY AND PHILOSOPHY OF INFINITY (August 2015), pp. 2463-2488 (26 pages) We review different conceptions of the set-theoretic multiverse and evaluate ...