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pro vyhledávání: '"Hirst, Jeffry L."'
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:
Davis, Caleb, Hirschfeldt, Denis R., Hirst, Jeffry L., Pardo, Jake, Pauly, Arno, Yokoyama, Keita
We consider two combinatorial principles, ${\sf{ERT}}$ and ${\sf{ECT}}$. Both are easily proved in ${\sf{RCA}}_0$ plus ${\Sigma^0_2}$ induction. We give two proofs of ${\sf{ERT}}$ in ${\sf{RCA}}_0$, using different methods to eliminate the use of ${\
Externí odkaz:
http://arxiv.org/abs/1812.09943
Autor:
Hirst, Jeffry L.
Finding the set of leaves for an unbounded tree is a nontrivial process in both the Weihrauch and reverse mathematics settings. Despite this, many combinatorial principles for trees are equivalent to their restrictions to trees with leaf sets. For ex
Externí odkaz:
http://arxiv.org/abs/1812.09762
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:
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
We prove that the statement "there is a $k$ such that for every $f$ there is a $k$-bounded diagonally non-recursive function relative to $f$" does not imply weak K\"onig's lemma over $\mathrm{RCA}_0 + \mathrm{B}\Sigma^0_2$. This answers a question po
Externí odkaz:
http://arxiv.org/abs/1401.3823
The enterprise of comparing mathematical theorems according to their logical strength is an active area in mathematical logic. In this setting, called reverse mathematics, one investigates which theorems provably imply which others in a weak formal t
Externí odkaz:
http://arxiv.org/abs/1212.0157
We present some results about generics for computable Mathias forcing. The $n$-generics and weak $n$-generics in this setting form a strict hierarchy as in the case of Cohen forcing. We analyze the complexity of the Mathias forcing relation, and show
Externí odkaz:
http://arxiv.org/abs/1201.6084
Autor:
Hirst, Jeffry L., Mummert, Carl
Publikováno v:
Notre Dame J. Formal Logic Volume 52, Number 2 (2011), 149-162
We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$ sentence of a cer
Externí odkaz:
http://arxiv.org/abs/1010.5165