10 citations · 82 across the 40 of their papers we have counts for
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A Note on the Decidability of the Necessity of Axioms
Merlin Carl
A typical kind of question in mathematical logic is that for the necessity of a certain axiom: Given a proof of some statement in some axiomatic system , one looks for minim…
The Lost Melody Phenomenon
Merlin Carl
A typical phenomenon for machine models of transfinite computations is the existence of so-called lost melodies, i.e. real numbers such that the characteristic function of the…
A note on Autoreducibility for Infinite Time Register Machines and parameter-free Ordinal Turing Machines
Merlin Carl
We propose a notion of autoreducibility for infinite time computability and explore it and its connection with a notion of randomness for infinite time machines.
Structures Associated with Real Closed Fields and the Axiom of Choice
Merlin Carl
An integer part I of a real closed field K is a discretely ordered subring with minimal element 1 such that, for every x in K, I contains some i such that x is between i and i+1 in…
Algorithmic Randomness for Infinite Time Register Machines
Merlin Carl
A concept of randomness for infinite time register machines (ITRMs), resembling Martin-Löf-randomness, is defined and studied. In particular, we show that for this notion of random…