• Media type: E-Article
  • Title: Strongly Amorphous Sets and Dual Dedekind Infinity
  • Contributor: Goldstern, Martin
  • Published: Wiley, 1997
  • Published in: Mathematical Logic Quarterly
  • Extent: 39-44
  • Language: English
  • DOI: 10.1002/malq.19970430105
  • ISSN: 0942-5616; 1521-3870
  • Keywords: Logic
  • Abstract: <jats:title>Abstract</jats:title><jats:p>1. If <jats:italic>A</jats:italic> is strongly amorphous (i.e., all relations on <jats:italic>A</jats:italic> are definable), then its power set <jats:italic>P(A)</jats:italic> is dually Dedekind infinite, i. e., every function from <jats:italic>P(A)</jats:italic> onto <jats:italic>P(A)</jats:italic> is injective. 2. The class of “inexhaustible” sets is not closed under supersets unless AC holds.</jats:p>
  • Description: <jats:title>Abstract</jats:title><jats:p>1. If <jats:italic>A</jats:italic> is strongly amorphous (i.e., all relations on <jats:italic>A</jats:italic> are definable), then its power set <jats:italic>P(A)</jats:italic> is dually Dedekind infinite, i. e., every function from <jats:italic>P(A)</jats:italic> onto <jats:italic>P(A)</jats:italic> is injective. 2. The class of “inexhaustible” sets is not closed under supersets unless AC holds.</jats:p>
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