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  1. On unfoldable cardinals, ω-closed cardinals, and the beginning of the inner model hierarchy.P. D. Welch - 2004 - Archive for Mathematical Logic 43 (4):443-458.
    Let κ be a cardinal, and let H κ be the class of sets of hereditary cardinality less than κ ; let τ (κ) > κ be the height of the smallest transitive admissible set containing every element of {κ}∪H κ . We show that a ZFC-definable notion of long unfoldability, a generalisation of weak compactness, implies in the core model K, that the mouse order restricted to H κ is as long as τ. (It is known that some weak (...)
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  • Determinacy in the difference hierarchy of co-analytic sets.P. D. Welch - 1996 - Annals of Pure and Applied Logic 80 (1):69-108.
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  • On elementary embeddings from an inner model to the universe.J. Vickers & P. D. Welch - 2001 - Journal of Symbolic Logic 66 (3):1090-1116.
    We consider the following question of Kunen: Does Con(ZFC + ∃M a transitive inner model and a non-trivial elementary embedding j: M $\longrightarrow$ V) imply Con (ZFC + ∃ a measurable cardinal)? We use core model theory to investigate consequences of the existence of such a j: M → V. We prove, amongst other things, the existence of such an embedding implies that the core model K is a model of "there exists a proper class of almost Ramsey cardinals". Conversely, (...)
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