Abstract
We describe a Borel poset satisfying the σ-finite chain condition but failing to satisfy the σ-bounded chain condition.
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B. Balcar, T. Pazak and E. Thümmel, On Todorcevic orderings, preprint (2012).
T. Bartoszyński, Set Theory: On the Structure of the Real Line, A. K. Peters Ltd. (Wellesley, MA, 1995).
A. Horn and A. Tarski, Measures in Boolean algebras, Trans. Amer. Math. Soc., 64 (1948), 467–497.
T. Jech, Set Theory, 3rd ed., revised and expanded, Springer Monographs in Mathematics, Springer-Verlag (Berlin, 2003).
N. Kalton, The Maharam problem, in: Séminaire d’Initiation à l’Analyse, Publ. Math. Univ. Pierre et Marie Curie 94, Univ. Paris VI (Paris, 1989), pp. Exp. No. 18, 13.
D. Maharam, An algebraic characterization of measure algebras, Ann. of Math., 48 (1947), 154–167.
M. Talagrand, Maharam’s problem, Ann. of Math., 168 (2008), 981–1009.
E. Thümmel, The problem of Horn and Tarski, preprint (2012).
S. Todorcevic, Two examples of Borel partially ordered sets with the countable chain condition, Proc. Amer. Math. Soc., 112 (1991), 1125–1128.
S. Todorcevic, A problem of von Neumann and Maharam about algebras supporting continuous submeasures, Fund. Math., 183 (2004), 169–183.
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Todorcevic, S. A Borel solution to the Horn–Tarski problem. Acta Math Hung 142, 526–533 (2014). https://doi.org/10.1007/s10474-013-0362-4
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DOI: https://doi.org/10.1007/s10474-013-0362-4