| | Gödel took [[set theory]] originally developed by [[Georg Cantor]] to new heights, as explained by Boston University Professors Juliet Floyd and Akihiro Kanamori in "How Gödel Transformed Set Theory": | | Gödel took [[set theory]] originally developed by [[Georg Cantor]] to new heights, as explained by Boston University Professors Juliet Floyd and Akihiro Kanamori in "How Gödel Transformed Set Theory": |
| | {{cquote|How Gödel transformed set theory can be broadly cast as follows: On the larger stage, from the time of Cantor, sets began making their way into topology, algebra, and analysis so that by the time of Gödel, they were fairly entrenched in the structure and language of mathematics. But how were sets viewed among set theorists, those investigating sets as such? Before Gödel, the main concerns were what sets are and how sets and their axioms can serve as a reductive basis for mathematics. Even today, those preoccupied with ontology, questions of mathematical existence, focus mostly upon the set theory of the early period. After Gödel, the main concerns became what sets do and how set theory is to advance as an autonomous field of mathematics.<ref>www.ams.org/notices/200604/fea-kanamori.pdf | | {{cquote|How Gödel transformed set theory can be broadly cast as follows: On the larger stage, from the time of Cantor, sets began making their way into topology, algebra, and analysis so that by the time of Gödel, they were fairly entrenched in the structure and language of mathematics. But how were sets viewed among set theorists, those investigating sets as such? Before Gödel, the main concerns were what sets are and how sets and their axioms can serve as a reductive basis for mathematics. Even today, those preoccupied with ontology, questions of mathematical existence, focus mostly upon the set theory of the early period. After Gödel, the main concerns became what sets do and how set theory is to advance as an autonomous field of mathematics.<ref>www.ams.org/notices/200604/fea-kanamori.pdf |