Abstract
Given a stationary subset T of \(\omega_{1}\), let \(\tilde{T}\) be the set of ordinals in the interval \((\omega_{1}, \omega_{2})\) which are necessarily in the image of T by any embedding derived from the nonstationary ideal. We consider the question of the size of \(\tilde{T}\), givenT, and use Martin's Maximum and \(\mathbb{P}_{max}\) to give some answers.
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