This National Science Foundation Project Grant award of $222,314 supports collaborative research on definability and computability over arithmetically significant fields at The Ohio State University from July 2022 through June 2025. The research will consider several problems in definability and computability over fields important to number theory, algebraic geometry, model theory, computability theory and valuation theory. Specifically, the principal investigators intend to study computability and definability in the first-order and existential language of rings over number fields, their rings of integers and their infinite algebraic extensions. Another set of related problems concerns computability and definability over function fields and rings of all characteristics. The research addresses outstanding questions regarding extensions of Hilbert's Tenth Problem to fields of rational numbers and rings of algebraic integers. The award furthers the goals of the Mathematical and Physical Sciences program of the National Science Foundation to strengthen the nation's scientific enterprise through increasing mathematical knowledge and understanding major problems.
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