In spite of the dramatic effect the discovery of infinite cardinals had on mathematics, some of the simplest questions regarding their arithmetic remained unanswered, such as how large the continuum is. . The chaotic world-view which emerged after Cohen's and Easton's independence results was challenged some years later by Silver's theorem about powers of singulars, and eventually by Shelah's work on cardinal arithmetic, which restored a dimension of order and regularity to the arithmetic of singular cardinals. The current project employs set theoretic methods, especially those infinite combinatorics discovered in the context of cardinal arithmetic, to study a variety of phenomena in infinite mathematical structures, such as embeddability and homogeneity.
Infinite cardinals have their own . . .
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