The Journal of Symbolic Logic

Research Article

On a result of Szemerédi

Albin L. Jones

2153 Oakdale Rd. Pasadena, MD 21122, USA, E-mail:, URL:


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 This generalizes an unpublished result of E. Szemerédi that Martin's axiom implies that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.

(Received July 05 2007)

Key words and phrases

  • cardinal numbers;
  • filter bases;
  • ordinal numbers;
  • polarized partitions;
  • pseudo-intersection number;
  • Ramsey theory