Set Theory. Recent Trends And Applications

Set theory started with a paper of Georg Cantor published on Crelle’s Journal in 1874, and was developed in the following decades by Cantor himself and many other mathematicians, including Dedekind, Gödel, von Neuman, and Zermelo. By the middle of the twentieth century, set theory had become the common language in which all mathematics is formulated, but it was only after Paul Cohen’s work on the Continuum Hypothesis in 1963 that the subject reached full maturity. After Cohen’s seminal work, a veritable explosion of results followed, and now, some forty years after, there is no sign of slowing down, with a seeming inexhaustible slew of new techniques and ideas, and unexpected applications to other areas of mathematics.Set theory started with a paper of Georg Cantor published on Crelle’s Journal in 1874, and was developed in the following decades by Cantor himself and many other mathematicians, including Dedekind, Gödel, von Neuman, and Zermelo. By the middle of the twentieth century, set theory had become the common language in which all mathematics is formulated, but it was only after Paul Cohen’s work on the Continuum Hypothesis in 1963 that the subject reached full maturity. After Cohen’s seminal work, a veritable explosion of results followed, and now, some forty years after, there is no sign of slowing down, with a seeming inexhaustible slew of new techniques and ideas, and unexpected applications to other areas of mathematics.