Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Mummert, Carl"'
Autor:
Hirst, Jeffry L., Mummert, Carl
Publikováno v:
Computability 12 (2023) 203-225
In this paper, methods of second order and higher order reverse mathematics are applied to versions of a theorem of Banach that extends the Schroeder-Bernstein theorem. Some additional results address statements in higher order arithmetic formalizing
Externí odkaz:
http://arxiv.org/abs/2303.05355
Autor:
Mummert, Carl
K\"onig's edge coloring theorem says that a bipartite graph with maximal degree $n$ has an edge coloring with no more than $n$ colors. We explore the computability theory and Reverse Mathematics aspects of this theorem. Computable bipartite graphs wi
Externí odkaz:
http://arxiv.org/abs/2008.12694
Autor:
Hirst, Jeffry L., Mummert, Carl
We show that RT(2,4) cannot be proved with one typical application of RT(2,2) in an intuitionistic extension of RCA0 to higher types, but that this does not remain true when the law of the excluded middle is added. The argument uses Kohlenbach's axio
Externí odkaz:
http://arxiv.org/abs/1611.03134
Autor:
Hirst, Jeffry L., Mummert, Carl
Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of some basi
Externí odkaz:
http://arxiv.org/abs/1604.04912
Publikováno v:
JiYoon Jung, Carl Mummert, Elizabeth Niese, and Michael Schroeder, "On erasure combinatorial batch codes'', Advances in Mathematics of Communications v. 12 n. 1, 2018, pp. 49-65
Combinatorial batch codes were defined by Paterson, Stinson, and Wei as purely combinatorial versions of the batch codes introduced by Ishai, Kushilevitz, Ostrovsky, and Sahai. There are $n$ items and $m$ servers, each of which stores a subset of the
Externí odkaz:
http://arxiv.org/abs/1511.04580
Autor:
Mummert, Carl
Thesis (Ph.D.)--Pennsylvania State University, 2005.
Mode of access: World Wide Web.
Mode of access: World Wide Web.
Publikováno v:
Computability, vol. 4, no. 2, pp. 103-117, 2015
We study the reverse mathematics and computability of countable graph theory, obtaining the following results. The principle that every countable graph has a connected component is equivalent to $\mathsf{ACA}_0$ over $\mathsf{RCA}_0$. The problem of
Externí odkaz:
http://arxiv.org/abs/1406.4786
Publikováno v:
Archive for Mathematical Logic May 2015, Volume 54, Issue 3-4, pp 425-437
The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to formalize the
Externí odkaz:
http://arxiv.org/abs/1401.0648
Autor:
Dzhafarov, Damir D., Mummert, Carl
We study the reverse mathematics of the principle stating that, for every property of finite character, every set has a maximal subset satisfying the property. In the context of set theory, this variant of Tukey's lemma is equivalent to the axiom of
Externí odkaz:
http://arxiv.org/abs/1109.3378
Autor:
Dzhafarov, Damir D., Mummert, Carl
Publikováno v:
Israel Journal of Mathematics, August 2013, Volume 196, Issue 1, pp 345-361
We study the logical content of several maximality principles related to the finite intersection principle ($F\IP$) in set theory. Classically, these are all equivalent to the axiom of choice, but in the context of reverse mathematics their strengths
Externí odkaz:
http://arxiv.org/abs/1109.3374