Fences, their endpoints, and projective Fraïssé theory
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- by Gianluca Basso and Riccardo Camerlo PDF
- Trans. Amer. Math. Soc. 374 (2021), 4501-4535 Request permission
Abstract:
We introduce a new class of compact metrizable spaces, which we call fences, and its subclass of smooth fences. We isolate two families $\mathcal {F}, \mathcal {F}_{0}$ of Hasse diagrams of finite partial orders and show that smooth fences are exactly the spaces which are approximated by projective sequences from $\mathcal {F}_{0}$. We investigate the combinatorial properties of Hasse diagrams of finite partial orders and show that $\mathcal {F}, \mathcal {F}_{0}$ are projective Fraïssé families with a common projective Fraïssé limit. We study this limit and characterize the smooth fence obtained as its quotient, which we call a Fraïssé fence. We show that the Fraïssé fence is a highly homogeneous space which shares several features with the Lelek fan, and we examine the structure of its spaces of endpoints. Along the way we establish some new facts in projective Fraïssé theory.References
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Additional Information
- Gianluca Basso
- Affiliation: Département des Opérations, Université de Lausanne, Quartier UNIL-Chambronne Bâtiment Anthropole, 1015 Lausanne, Switzerland
- Address at time of publication: Institut Camille Jordan, Université Claude Bernard Lyon 1, Université de Lyon, 43, boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France
- MR Author ID: 1247093
- ORCID: 0000-0001-8150-9770
- Email: basso@math.univ-lyon1.fr
- Riccardo Camerlo
- Affiliation: Dipartimento di matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy
- MR Author ID: 663257
- Email: camerlo@dima.unige.it
- Received by editor(s): March 8, 2020
- Received by editor(s) in revised form: December 10, 2020
- Published electronically: March 30, 2021
- Additional Notes: The first author’s work was conducted as a doctoral student at Univerisité de Lausanne and Università di Torino, and partially within the program “Investissements d’Avenir” (ANR-16-IDEX-0005) operated by the French National Research Agency (ANR)
The research of the second author was partially supported by PRIN 2017NWTM8R - “Mathematical logic: models, sets, computability”. - © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 4501-4535
- MSC (2020): Primary 03E15; Secondary 54F50, 54F65
- DOI: https://doi.org/10.1090/tran/8366
- MathSciNet review: 4251237