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Q&A for professional mathematicians
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Hottest Questions Today - MathOverflow
Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, ...
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Let $A$ be a $C^*$-algebra and $(a_{ij}) \in M_n(A)$ be a positive matrix. Does there exist a constant $C \ge 0$ (not depending on the $a_{ij}$) such that $$\lVert(a_{ij})\rVert \le C \Bigl\lVert\s...
Mathoverflow.net news digest
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4 months
Examples of use of ordinal computability / ordinals in classical recursion theor...
I am a PhD student and in the process of making a talk to my team of research, I am looking for examples of usage of ordinals or ordinal computability (via ITTMs or other models) in regular (non infinite time) computability. I so far have two examples...
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4 years
Are ITTM's necessary to compute Turing's "computable numbers" and what does that...
In his celebrated paper, "On Computable Numbers, With An Application To the Entscheidungsproblem", Turing defines a "computable number" as follows:
The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by finite means....According to my definition, a number is computable if its decimal can be written down by a machine.... -
8 years
Can you consistently add axioms about the Busy Beaver function to ZF?
Consider a Turing Machine with $N$ states which checks all theorems of ZF and halts upon finding a contradiction. If ZF were consistent and could prove the value of $BusyBeaver(N)$, then it would be able to prove its own consistency, which Gödel proved...
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15 years
Turing Machine which generates order on the set of its states
This question is related to this one Do Turing Machines generates any nontrivial lattice on the set o symbols or states?
The Turing machine (TM) is an abstract model for effective implementation of (finite algorithmic) calculation. TM is defined over some alphabet of symbols L and reading data performs a finite sequence of operations on these symbols in the manner described...
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