Zobrazeno 1 - 10
of 120
pro vyhledávání: '"Solomon, Reed"'
The Ginsburg--Sands theorem from topology states that every infinite topological space has an infinite subspace homeomorphic to exactly one of the following five topologies on $\omega$: indiscrete, discrete, initial segment, final segment, and cofini
Externí odkaz:
http://arxiv.org/abs/2402.05990
We study versions of the tree pigeonhole principle, $\mathsf{TT}^1$, in the context of Weihrauch-style computable analysis. The principle has previously been the subject of extensive research in reverse mathematics. Two outstanding questions from the
Externí odkaz:
http://arxiv.org/abs/2312.10535
We introduce the notion of the \emph{first-order part} of a problem in the Weihrauch degrees. Informally, the first-order part of a problem $\mathsf{P}$ is the strongest problem with codomaixn $\omega$ that is Weihrauch reducible to $\mathsf{P}$. We
Externí odkaz:
http://arxiv.org/abs/2301.12733
Autor:
Dzhafarov, Damir D.1 (AUTHOR) damir@math.uconn.edu, Solomon, Reed1 (AUTHOR), Yokoyama, Keita2 (AUTHOR)
Publikováno v:
Computability. Jan2024, p1-13. 13p.
Autor:
Franklin, Johanna N. Y., Solomon, Reed
We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune-free degrees, low
Externí odkaz:
http://arxiv.org/abs/1909.06003
We study the implications of model completeness of a theory for the effectiveness of presentations of models of that theory. It is immediate that for a computable model $\mathcal A$ of a computably enumerable, model complete theory, the entire elemen
Externí odkaz:
http://arxiv.org/abs/1903.00734
Publikováno v:
J. symb. log. 85 (2020) 166-198
We define the notion of a determined Borel code in reverse math, and consider the principle $DPB$, which states that every determined Borel set has the property of Baire. We show that this principle is strictly weaker than $ATR$. Any $\omega$-model o
Externí odkaz:
http://arxiv.org/abs/1809.03940
Autor:
Csima, Barbara F., Dzhafarov, Damir D., Hirschfeldt, Denis R., Jockusch, Jr., Carl G., Solomon, Reed, Westrick, Linda Brown
Hindman's Theorem (HT) states that for every coloring of $\mathbb N$ with finitely many colors, there is an infinite set $H \subseteq \mathbb N$ such that all nonempty sums of distinct elements of $H$ have the same color. The investigation of restric
Externí odkaz:
http://arxiv.org/abs/1804.09809
We analyze the Dual Ramsey Theorem for $k$ partitions and $\ell$ colors ($\mathsf{DRT}^k_\ell$) in the context of reverse math, effective analysis, and strong reductions. Over $\mathsf{RCA}_0$, the Dual Ramsey Theorem stated for Baire colorings is eq
Externí odkaz:
http://arxiv.org/abs/1710.00070
The principle $ADS$ asserts that every linear order on $\omega$ has an infinite ascending or descending sequence. This has been studied extensively in the reverse mathematics literature, beginning with the work of Hirschfeldt and Shore. We introduce
Externí odkaz:
http://arxiv.org/abs/1605.06164