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A Michael Space in the Laver model

Primarily AI-generated textHuman understanding: no partsmath.LO — Logic

Contributed by Morgan Jones ↗

Version 1 / Nov 11, 2026 / CC BY 4.0

Abstract

We show that a Michael space exists in the Laver model.

Author comments: I was stress testing Claude Fable 5.2 with varying levels of problems and trying to improve my workflow with AI. This problem was reasoned pretty quickly by Claude, however it required some convincing that it could do it.

Provenance statement

Claude Fable 5.2 was given the statement of the conjecture. It took some prompting and reasoning but it did it on the third round of attempts after some hemming and hawing. I have not attached my name onto the paper because I didn't do anything.

Tools used

Anthropic
Claude FableVersion 5.2

References

  1. K. Alster, The product of a Lindelöf space with the space of irrationals under Martin's axiom , Proc. Amer. Math. Soc. 110 (1990), 543--547.
  2. T. Bartoszyński and H. Judah, Set theory: on the structure of the real line , A K Peters, Wellesley, MA, 1995.
  3. M. Goldstern, Tools for your forcing construction , in: Set theory of the reals (Ramat Gan, 1991), Israel Math. Conf. Proc. 6 , Bar-Ilan Univ., 1993, 305--360.
  4. R. Laver, On the consistency of Borel's conjecture , Acta Math. 137 (1976), 151--169.
  5. L. B. Lawrence, The influence of a small cardinal on the product of a Lindelöf space and the irrationals , Proc. Amer. Math. Soc. 110 (1990), 535--542.
  6. A. Martínez-Celis, Michael spaces and ultrafilters , preprint, arXiv:2310.02749.arXiv
  7. E. Michael, The product of a normal space and a metric space need not be normal , Bull. Amer. Math. Soc. 69 (1963), 375--376.
  8. A. W. Miller, There are no Q-points in Laver's model for the Borel conjecture , Proc. Amer. Math. Soc. 78 (1980), 103--106.
  9. A. W. Miller and B. Tsaban, Point-cofinite covers in the Laver model , Proc. Amer. Math. Soc. 138 (2010), 3313--3321.
  10. J. T. Moore, Some of the combinatorics related to Michael's problem , Proc. Amer. Math. Soc. 127 (1999), 2459--2467.
Show all 11 referencesShow fewer references
  1. D. Repovš and L. Zdomskyy, Products of Hurewicz spaces in the Laver model , Bull. Symb. Log. 23 (2017), 324--333.

Version history

  1. v1 · 10 pagesSubmitted by Morgan JonesI was stress testing Claude Fable 5.2 with varying levels of problems and trying to improve my workflow with AI. This problem was reasoned pretty quickly by Claude, however it required some convincing that it could do it.CurrentNov 10, 2026