Non-existence of Universal Orders in Many Cardinals

Menachem Kojman, Saharon Shelah

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Abstract

Our theme is that not every interesting question in set theory is independent of $ZFC$. We give an example of a first order theory $T$ with countable $D(T)$ which cannot have a universal model at $\aleph_1$ without CH; we prove in $ZFC$ a covering theorem from the hypothesis of the existence of a universal model for some theory; and we prove --- again in ZFC --- that for a large class of cardinals there is no universal linear order (e.g. in every $\aleph_1
Original languageEnglish
Pages (from-to)875-891
JournalJournal of Symbolic Logic
Volume57
Issue number3
DOIs
StatePublished - 1992

Keywords

  • Mathematics - Logic

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