Abstract
In his seminal paper introducing the fine structure of L, Jensen (Ann Math Log 4:229–308, 1972) proved that under \(V=L\) any regular cardinal that reflects stationary sets is weakly compact. In this paper we give a new proof of Jensen’s result that is straight-forward and accessible to those without a knowledge of Jensen’s fine structure theory. The proof here instead uses hyperfine structure, a very natural and simpler alternative to fine structure theory introduced by Friedman and Koepke (Bull Symb Log 3:453–468, 1997).
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Notes
Although the idea of the trace is implicit in the proof of the main theorem in [1] it is not isolated as a concept there.
References
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Acknowledgements
This research was conducted under the supervision of Philip Welch with the support of an EPSRC Doctoral Training Grant Studentship, and further support from a JSPS Postdoctoral Fellowship for Research in Japan. I would like to thank an anonymous referee for detailed and valuable suggestions to improve the clarity of this article.
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Brickhill, H. Square below a non-weakly compact cardinal. Arch. Math. Logic 59, 409–426 (2020). https://doi.org/10.1007/s00153-019-00695-6
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DOI: https://doi.org/10.1007/s00153-019-00695-6