This is a collection of 31 papers based on invited lectures presented at the International Munich Centenary Conference in 2001. The contributors include historians of mathematics and researchers in set theory, mathematical logic, foundations of mathematics and philosophy of mathematics. This volume presents a unique opportunity to learn the views of prominent mathematicians and philosophers of science on the foundations of mathematics. Due to space limitations, I will mention only a sample of articles. Wodin’s paper is a readable introduction to his Ω-logic, by which he is able to decide the continuum hypothesis. Friedman presents a set theory, in which the schema of comprehension is modified in a different way than in ZFC and which has the strength of ZFC augmented with a class of subtle cardinals. Hauser’s paper is an interesting essay about the search for new axioms for set theory and the role of large cardinals in this process. A historical study by Peckhaus expounds what was known about paradoxes in set theory in Göttingen around the time of Russell's discovery of his paradox and mentions Zermelo's independent discovery of this paradox.

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