From the 3 of 16 linked papers with an AI index.
16 papers
HJ numbers revisited
Saharon Shelah
The paper sharpens the upper bounds for Hales‑Jewett numbers, proving they can be bounded by a tower of only two exponentiations instead of the previously much larger iterated towe…
From Shelah's block-content to Hales-Jewett
Mohammad Golshani, Mostafa Mirabi, Saharon Shelah
The paper establishes a quantitative equivalence between Hales‑Jewett numbers and Shelah’s block‑content canonization, showing that block canonization together with the Gallai‑Witt…
Limit laws for component-pruned sparse random graphs and percolated tori
Mostafa Mirabi, Saharon Shelah
The paper establishes monadic second‑order (MSO₂) zero‑one laws for very sparse Erdős–Rényi graphs after deleting small components, and derives first‑order limit laws for bond perc…
Discontinuous homomophisms without Hamel bases
Paul Larson, Saharon Shelah
We produce a model of ZF + DC in which there exists a discontinuous homomorphism from the real line to itself but no Hamel basis for the real line, and prove a generalization of th…
Model-theoretic Tameness in finite extensions of groups
Yatir Halevi, Saharon Shelah
It is shown that finite-index extensions and finite-index subgroups of -stable groups can be model-theoretically wild. More precisely, there exists an -stable group suc…
On the problem of stability of abstract elementary classes of modules
Gianluca Paolini, Saharon Shelah
It is an open problem of Mazari-Armida whether every abstract elementary class of -modules , with the pure submodule r…