Mathematical Sciences: Foundations of Mathematics

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Investigations will be pursued into: (i) The priority method as applied to recursively enumerable Turing degrees and automorphisms of the r.e. sets; (ii) Superstable theories and Lachlan's conjecture on homogeneous structures; (iii) Mathematical ideas in the sense of ideas which admit formalization. Such foundational studies have the potential of clarifying our thoughts and have sometimes carried over into theoretical computer science.