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math.LO2023★ 1 cited
Conway and Doyle Can Divide by Three, But I Can't
Patrick Lutz
Conway and Doyle have claimed to be able to divide by three. We attempt to replicate their achievement and fail. In the process, we get tangled up in some shoes and socks and forge…
math.LO2023
A theory satisfying a strong version of Tennenbaum's theorem
Patrick Lutz, James Walsh
We answer a question of Pakhomov by showing that there is a consistent, c.e. theory such that no theory which is definitionally equivalent to has a computable model. A key…
math.LO2023
Martin's conjecture for regressive functions on the hyperarithmetic degrees
Patrick Lutz
We answer a question of Slaman and Steel by showing that a version of Martin's conjecture holds for all regressive functions on the hyperarithmetic degrees. A key step in our proof…