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    Garti, Shimon 2015. Dense Free Sets. Order,


On a result of Szemerédi

  • Albin L. Jones (a1)
  • DOI:
  • Published online: 01 March 2014

We provide a short proof that if κ is a regular cardinal with κ < c, then

for any ordinal α < min{, κ}. In particular,

for any ordinal α < . This generalizes an unpublished result of E. Szemerédi that Martin's axiom implies that

for any cardinal κ with κ < c.

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[3]P. Erdős and R. Rado , A partition calculus in set theory, Bulletin of the American Mathematical Society, vol. 62 (1956), pp. 427489.

[6]E. K. van Douwen , The integers and topology, Handbook of set theoretic topology (K. Kunen and J. E. Vaughan , editors), North-Holland, Amsterdam, 1984, pp. 111167.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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