Open Problems in Mathematical Logic — Problem 17

Definitions and mathematical statement

The supplied record asks for further pairs $(M,\mathbb{P})$, where $M$ is a model and $\mathbb{P}\in M$ is a forcing notion, satisfying a condition denoted by $(*)$. Its statement is:

Find more models $M$ and forcing notions $\mathbb{P}\in M$ such that $(*)$ is true.

The condition $(*)$ is not defined in the supplied record. Neither the theory satisfied by $M$ nor any additional hypotheses on $M$ or $\mathbb{P}$ are specified. Moreover, the examples relative to which further examples are requested are absent. Thus this is an incomplete formulation: the intended condition and the relevant background hypotheses must be recovered before a precise mathematical problem can be stated. No interpretation of $(*)$, model domain, or additional forcing hypothesis is imposed here.

Short English statement

The source requests additional models and forcing notions belonging to those models that satisfy a condition labelled $(*)$. Because that condition and the surrounding hypotheses are missing, the intended mathematical target cannot be specified precisely from this record.

Sources

• Local UnsolvedMath registry, permanent ID $801005$, source problem code catalogue entry, title: Open Problems in Mathematical Logic --- Problem 17. The registry attributes the problem to Barmpalias, Gao et al., with proposed year 2026, and labels it open; this is supplied source metadata, not an independently verified status assessment.
• Barmpalias, Gao et al., Open Problems in Mathematical Logic (2026), Problem 17. Supplied source URL: https://arxiv.org/abs/2608.26628. This reference is supplied attribution; its contents have not been independently consulted for this draft.
• Supplied provenance records access on 2026-10-16 and extraction by arxiv_latex. This date describes the supplied provenance, not an independent source visit or verification performed for this draft.