Infinite subsets of random sets of integers

• Autores: Bjorn Kjos Hanssen
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 16, Nº 1, 2009, págs. 103-110
• Idioma: inglés
• DOI: 10.4310/mrl.2009.v16.n1.a10
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• Resumen

  • There is an infinite subset of a Martin-L\"of random set of integers that does not compute any Martin-L\"of random set of integers. To prove this, we show that each real of positive effective Hausdorff dimension computes an infinite subset of a Martin-L\"of random set of integers, and apply a result of Miller.