Counterexamples to the Generalized Gaifman Conjecture

Yi Zhang

Abstract

Shelah and Usvyatsov proposed the Generalized Gaifman Conjecture [SU25, Conjecture 1.1]. We give a negative answer.

Disclosure

“and IT (λ, µ) = sup IT (λ, N ) : N |= T P , |N | = µ . We replace their displayed maxi- mum by a supremum. LLM disclosure The author found the proof with the assistance of ChatGPT. The author takes full responsibility for the entire content of the paper.”

PDF page 1
Classification
Substantial proof generation
Multiplier
10
Verified

Structural counts

Pages 4 pdf
Theorems 3 source
Lemmas 0 source
Propositions 3 source
Corollaries 0 source
Definitions 0 source
Displayed equations 1 source
Bibliography entries 10 source
Appendix pages 0 estimated

Count notes

  • Source counts use the expanded primary TeX file main.tex.
  • Appendix pages include the first PDF page with an explicit Appendix heading through the final page.