• Corpus ID: 237513458

Non-absoluteness of Hjorth's Cardinal Characterization

  title={Non-absoluteness of Hjorth's Cardinal Characterization},
  author={Philipp Lucke and Ioannis A. Souldatos},
In [5], Hjorth proved that for every countable ordinal α, there exists a complete Lω1,ω-sentence φα that has models of all cardinalities less than or equal to אα, but no models of cardinality אα+1. Unfortunately, his solution does not yield a single Lω1,ω-sentence φα, but a set of Lω1,ω-sentences, one of which is guaranteed to work. It was conjectured in [9] that it is independent of the axioms of ZFC which of these sentences has the desired property. In the present paper, we prove that this… 


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