Remarkable cardinals
نویسندگان
چکیده
To a large extent, the scientific work of both Peter Koepke and Philip Welch has always been inspired by Ronald Jensen’s fine structure theory and his Covering Lemma for L, the constructible universe. Cf., e.g., their joint papers [5] and [6]. In this paper we aim to play with the theme that large cardinals compatible with “V=L,” specifically: remarkable cardinals, allow us to create situations below א2 which above א2 can only occur if Jensen’s Covering fails. Large cardinals are a central tool in set theory. A cardinal κ is called supercompact iff for every λ there is an elementary embedding j : V → M such that M is transitive, κ is the critical point of j, j(κ) > λ, and M ⊂M . The following elegant characterization of supercompact cardinals is due to Magidor, cf. [7].
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