9401275 Jech This research project will concentrate on set theory and on applications of set theory in algebra. The major topics of research will include left-distributive algebras, elementary embeddings, stationary sets, the theory of large cardinals, applications of forcing, the singular cardinals problem and the theory of possible cofinalities, countably complete filters and ideals, infinitary combinatorics, and problems in Boolean algebras. This research deals with the abstract mathematical discipline called SET THEORY. Set theory serves as the foundation for other mathematical disciplines such as topology, measure theory and functional analysis. Its study of abstract infinite sets provides an invaluable insight into the expressive power of modern mathematics and its limitations. In particular, modern set theory, with its emphasis on independence proofs and the theory of large cardinals, enables one to establish provability or unprovability and analyze the complexity of mathematical conjectures. ***
