On PCF spaces which are not Fréchet-Urysohn

• Autorzy: Martínez, J. C.
• Języki publikacji: EN

Abstrakty

EN

By means of a forcing argument, it was shown by Pereira that if CH holds then there is a separable PCF space of height ω1 + 1 which is not Fréchet-Urysohn. In this paper, we give a direct proof of Pereira’s theorem by means of a forcing-free argument, and we extend his result to PCF spaces of any height δ + 1 where δ<ω2 with cf(δ) = ω1.

Słowa kluczowe

EN

PCF space; sequentiality; Fréchet-Urysohn property

• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2018
• Tom: Vol. 53
• Strony: 67--77
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Martínez, J. C.

• Facultat de Matematiques i Informatica Universitat de Barcelona Gran Via 585, 08007 Barcelona, Spain ,

Bibliografia

• [1] U. Abraham and M. Magidor, Cardinal arithmetic, In: M. Foreman and A. Kanamori, editors, vol. 2 of Handbook of Set Theory, Springer, New York, 2010, pp. 1149–1227.
• [2] J. Bagaria, Thin-tall spaces and cardinal sequences, In: E. Pearl, editor, Open problems in Topology II, Elsevier, Amsterdam, 2007, pp. 115–124.
• [3] J.E. Baumgartner and S. Shelah, Remarks on superatomic Boolean algebras, Annals of Pure and Applied Logic 33:2 (1987), 109–129.
• [4] R. Bonnet and M. Rubin, On well-generated Boolean algebras, Annals of Pure and Applied Logic 105:1–3 (2000), 1–50.
• [5] M.R. Burke and M. Magidor, Shelah’s pcf theory and its applications, Annals of Pure and Applied Logic 50:3 (1990), 207–254.
• [6] K. Er-Rhaimini and B. Veliˇckovi´c, PCF structures of height less than ω3, The Journal of Symbolic Logic 75:4 (2010), 1231–1248.
• [7] M. Foreman, Some problems in singular cardinals combinatorics, Notre Dame Journal of Formal Logic 46:3 (2005), 309–322.
• [8] J.C. Mart´ınez, Cardinal sequences for superatomic Boolean algebras, In: S. Geschke, B. L¨owe and P. Schlicht, editors, Infinity, Computability and Metamathematics, vol. 23 of Tributes Series, pp. 273–284, College Publications, Milton Keynes, 2014.
• [9] L. Pereira, Applications of the topological representation of the pcf-structure, Archive for Mathematical Logic 47:5 (2008), 517–527.
• [10] J.C. Ruyle, Cardinal sequences of PCF structures, Ph.D. Thesis, University of California, Riverside, 1998.
• [11] S. Shelah, Cardinal arithmetic, vol. 29 of Oxford Logic Guides, Oxford University Press, 1994.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).

Identyfikatory

DOI

10.4467/20842589RM.18.004.8837