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math.LO2026
Categoricity without Power
Jun Le Goh, Chieu-Minh Tran
We prove an analogue of Morley's categoricity theorem where cardinality is replaced by the recursion-theoretic notion of arithmetic degree. We say that a complete arithmetically de…
math.CO2026
Finite combinatorics and computability theory
Damir D. Dzhafarov, Jun le Goh
We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reform…