Function-Space Measure Embedding Values

Definitions and mathematical statement

Let $\omega_1$ be the least uncountable ordinal and $\omega_2$ the next initial ordinal. Set \[ X={}^{\omega_1}\omega_1=\{f\mid f:\omega_1\to\omega_1\}. \] The supplied record refers to a particular "function-space measure" $\nu$ on $X$ and its associated elementary embedding $j_\nu$. It does not define this measure, specify the background axioms, or give the domain, codomain, or construction of the embedding. These are unresolved prerequisites; the statement below concerns the particular objects intended by the source.

Requested computation. For that intended measure and embedding, determine the ordinal \[ j_\nu(\omega_2). \] The reconstructed statement additionally asks for the values of $j_\nu$ on "relevant cardinals," but supplies no class of cardinals or precise quantifier for this extension.

Supplied contextual bound. The extracted original passage attributes to Chan a strict upper bound for $j_\nu(\omega_1)$. Its right-hand side is rendered as "$\delta$ 13" in the supplied extraction. This may denote $\delta^1_3$, but the indices and the intended invariant are not established by the supplied record. Consequently, neither that interpretation nor a definition of the bound is asserted here. The attribution and strictness of the reported inequality are retained as source information, not independently verified mathematical facts.

Short English statement

Determine $j_\nu(\omega_2)$ for the particular function-space measure on ${}^{\omega_1}\omega_1$ intended by the source. The measure, background axioms, and associated embedding require clarification. The broader request about other cardinals and the notation in a bound attributed to Chan also remain unresolved.

Sources

• Local UnsolvedMath registry: supplied source record, permanent ID $30006172$, exact source problem code catalogue entry, title "Function-Space Measure Embedding Values." The record belongs to the Oberwolfach Reports Open Problems collection and gives proposed year 2025; no proposer is identified.
• Supplied report citation: Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140. https://doi.org/10.4171/owr/2025/2.
• Supplied literature source: "Oberwolfach Report 2/2025." https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/online/10.4171-owr-2025-2.pdf.
• Literature assessment dated exactly 2026-08-22: the supplied curation labels the problem open and says the report requests the next embedding value while reporting only a strict upper bound for a lower value. This is supplied dated curation, not an independently verified assessment of the literature or current status.
• The registry labels the statement corrected_verified and says it was reconstructed and checked against the official report. Those are supplied provenance claims; no independent source verification is asserted here. The extracted passage attributes the lower-value bound to Chan, without a full name or separate bibliographic reference.