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math.LO2026
Free sets, thin sets and rainbows for barriers
Lorenzo Carlucci, Oriola Gjetaj
We formulate and prove the generalizations of Friedman's free set and thin set theorems and of the rainbow Ramsey theorem to colorings of barriers. We analyze the strength of these…
math.LO2026
Goodstein at the Second Threshold: An Independence Result for
Oriola Gjetaj, Andreas Weiermann
The classical Goodstein process, defined via hereditary base- exponential normal form, is a well-known example of a principle unprovable in Peano Arithmetic. In this paper, we g…