ZFC proves that the class of ordinals is not weakly compact for definable classes
In ZFC, the class Ord of ordinals is easily seen to satisfy the definable version of strong inaccessibility. Here we explore deeper ZFC-verifiable combinatorial properties of Ord, as indicated in Theorems A & B below. Note that Theorem A shows the unexpected result that Ord is never definably weakly compact in any model of ZFC.
Theorem A. Let be any model of ZFC.
(1)The definable tree property fails in : There is an -definable Ord-tree with no -definable cofinal branch.... Expand abstract
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- Association for Symbolic Logic
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- © The Association for Symbolic Logic 2018
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