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J. Vickers & P. D. Welch (2000). On Successors of Jónsson Cardinals.

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  1.  17
    Consistency Strength of Higher Chang's Conjecture, Without CH.Sean D. Cox - 2011 - Archive for Mathematical Logic 50 (7-8):759-775.
    We prove that ${(\omega_3, \omega_2) \twoheadrightarrow (\omega_2, \omega_1)}$ implies there is an inner model with a weak repeat measure.
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    Greatly Erdős Cardinals with Some Generalizations to the Chang and Ramsey Properties.I. Sharpe & P. D. Welch - 2011 - Annals of Pure and Applied Logic 162 (11):863-902.
    • We define a notion of order of indiscernibility type of a structure by analogy with Mitchell order on measures; we use this to define a hierarchy of strong axioms of infinity defined through normal filters, the α-weakly Erdős hierarchy. The filters in this hierarchy can be seen to be generated by sets of ordinals where these indiscernibility orders on structures dominate the canonical functions.• The limit axiom of this is that of greatly Erdős and we use it to calibrate (...)
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