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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.18502 |
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| _version_ | 1866910001027612672 |
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| author | Benhamou, Tom LeClair, Sean |
| author_facet | Benhamou, Tom LeClair, Sean |
| contents | We continue the study of probabilistic and topological properties of the set of reals that are being guessed by a diamond sequence from \cite{Benhamou_Wu}.
We show that the existence of sequence of a asymptotic growth $π$ which infinitely guesses a probability one set is equivalent to the divergence of $\sum_{n=0}^{\infty}\frac{π(n)}{2^n}$. We then provide concrete examples for guessing sequences of certain low asymptotic growth using random walks.
Finally, we show that the ultrafilter construction from \cite{Benhamou_Wu} always yield an ultrafilters and a sequence which guesses a meager set, while a simple construction using Cohen forcing gives a non-meager set of guessed reals. These results answer \cite[Question 6.13]{Benhamou_Wu} and partially addresses \cite[Question 6.8]{Benhamou_Wu}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18502 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Asymptotic Behavior of Guessing Sequences Benhamou, Tom LeClair, Sean Logic We continue the study of probabilistic and topological properties of the set of reals that are being guessed by a diamond sequence from \cite{Benhamou_Wu}. We show that the existence of sequence of a asymptotic growth $π$ which infinitely guesses a probability one set is equivalent to the divergence of $\sum_{n=0}^{\infty}\frac{π(n)}{2^n}$. We then provide concrete examples for guessing sequences of certain low asymptotic growth using random walks. Finally, we show that the ultrafilter construction from \cite{Benhamou_Wu} always yield an ultrafilters and a sequence which guesses a meager set, while a simple construction using Cohen forcing gives a non-meager set of guessed reals. These results answer \cite[Question 6.13]{Benhamou_Wu} and partially addresses \cite[Question 6.8]{Benhamou_Wu}. |
| title | On the Asymptotic Behavior of Guessing Sequences |
| topic | Logic |
| url | https://arxiv.org/abs/2601.18502 |