The weak diamond

Talk given at the Harvard logic seminar, September 18, 2019.

Abstract

The weak diamond is a combinatorial guessing principle which came out of Shelah's work on Whitehead's problem. It was introduced by Devlin and Shelah. As opposed to the usual diamond, weak diamond follows from the continuum hypothesis, and even just from strict monotonicity of cardinal exponentiation. I will give an introduction to the principle. Time permitting, I will also discuss using the weak diamond to obtain amalgamation properties in abstract model theory.

References

• Keith J. Devlin and Saharon Shelah, A weak version of ◊ which follows from 2^ℵ₀ < 2^ℵ₁, Israel Journal of Mathematics 29 (1978), 239–247.

• Sebastien Vasey, Accessible categories, set theory, and model theory: an invitation, Preprint: pdf arXiv.