Zobrazeno 1 - 10
of 127
pro vyhledávání: '"McNicholl, Timothy H."'
Autor:
McNicholl, Timothy H.
We study presentations of $C^*(X)$ that are evaluative over a presentation of $X$ in that $(f,p) \mapsto f(p)$ is computable. We prove existence-uniqueness theorems for such presentations. We use our methods to prove an effective Banach-Stone Theorem
Externí odkaz:
http://arxiv.org/abs/2403.13616
Autor:
Burton, Peter, Eagle, Christopher J., Fox, Alec, Goldbring, Isaac, Harrison-Trainor, Matthew, McNicholl, Timothy H., Melnikov, Alexander, Thewmorakot, Teerawat
We establish a computable version of Gelfand Duality. Under this computable duality, computably compact presentations of metrizable spaces uniformly effectively correspond to computable presentations of unital commutative $C^*$ algebras.
Externí odkaz:
http://arxiv.org/abs/2402.16672
Within the framework of computable infinitary continuous logic, we develop a system of hyperarithmetic numerals. These numerals are infinitary sentences in a metric language $L$ that have the same truth value in every interpretation of $L$. We prove
Externí odkaz:
http://arxiv.org/abs/2211.01181
We consider the complexity (in terms of the arithmetical hierarchy) of the various quantifier levels of the diagram of a computably presented metric structure. As the truth value of a sentence of continuous logic may be any real in $[0,1]$, we introd
Externí odkaz:
http://arxiv.org/abs/2106.05372
Autor:
McNicholl, Timothy H., Rojas, Diego A.
We establish a framework for the study of the effective theory of weak convergence of measures. We define two effective notions of weak convergence of measures on $\mathbb{R}$: one uniform and one non-uniform. We show that these notions are equivalen
Externí odkaz:
http://arxiv.org/abs/2106.00086
Autor:
Carlson, Marilyn P., O’Bryan, Alan E., Strayer, Jeremy F., McNicholl, Timothy H., Hagman, Jess E.
Publikováno v:
In Journal of Mathematical Behavior March 2024 73
Autor:
McNicholl, Timothy H.
We consider the question as to whether the exponent of a computably presentable Lebesgue space whose dimension is at least 2 must be computable. We show this very natural conjecture is true when the exponent is at least 2 or when the space is finite-
Externí odkaz:
http://arxiv.org/abs/1912.13087
We contribute to the program of extending computable structure theory to the realm of metric structures by investigating lowness for isometric isomorphism of metric structures. We show that lowness for isomorphism coincides with lowness for isometric
Externí odkaz:
http://arxiv.org/abs/1911.05899
Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.
Externí odkaz:
http://arxiv.org/abs/1906.12209
Autor:
McNicholl, Timothy H., Rojas, Diego A.
Publikováno v:
In Information and Computation January 2023 290