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MENAS’S CONJECTURE REVISITED
- Part of
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- Journal:
- Bulletin of Symbolic Logic / Volume 29 / Issue 3 / September 2023
- Published online by Cambridge University Press:
- 08 May 2023, pp. 354-405
- Print publication:
- September 2023
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- Article
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In an article published in 1974, Menas conjectured that any stationary subset of
can be split in 
many pairwise disjoint stationary subsets. Even though the conjecture was shown long ago by Baumgartner and Taylor to be consistently false, it is still haunting papers on 
. In which situations does it hold? How much of it can be proven in ZFC? We start with an abridged history of the conjecture, then we formulate a new version of it, and finally we keep weakening this new assertion until, building on the work of Usuba, we hit something we can prove.
WEAK SATURATION AND WEAK AMALGAMATION PROPERTY
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- Journal:
- The Journal of Symbolic Logic / Volume 84 / Issue 3 / September 2019
- Published online by Cambridge University Press:
- 04 July 2019, pp. 929-936
- Print publication:
- September 2019
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We study the two model-theoretic concepts of weak saturation and weak amalgamation property in the context of accessible categories. We relate these two concepts providing sufficient conditions for existence and uniqueness of weakly saturated objects of an accessible category
${\cal K}$. We discuss the implications of this fact in classical model theory.
