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- Denis R. Hirschfeldt, Carl G. Jockusch, Rutger Kuyper, Paul E. Schupp
- J. Symb. Log.
- 2016

A coarse description of a set A ⊆ ω is a set D ⊆ ω such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputable information can be effectively recovered from all coarse descriptions of a given set A, especially when A is effectively random in some sense. We show that if A is 1-random and B is computable… (More)

- Rutger Kuyper, Sebastiaan Terwijn
- Rew. Symb. Logic
- 2013

- Rutger Kuyper
- LFCS
- 2013

- Rutger Kuyper, Sebastiaan Terwijn
- J. Logic & Analysis
- 2014

We prove that a real x is 1-generic if and only if every differentiable computable function has continuous derivative at x. This provides a counterpart to recent results connecting effective notions of randomness with differentiability. We also consider multiply differentiable computable functions and polynomial time computable functions.

- Rutger Kuyper
- Arch. Math. Log.
- 2014

Skvortsova showed that there is a factor of the Medvedev lattice which captures intuitionistic propositional logic (IPC). However, her factor is unnatural in the sense that it is constructed in an ad hoc manner. We present a more natural example of such a factor. We also show that the theory of every non-trivial factor of the Medvedev lattice is contained… (More)

- Rutger Kuyper
- Ann. Pure Appl. Logic
- 2013

We give natural examples of factors of the Muchnik lattice which capture intuitionistic propositional logic (IPC), arising from the concepts of lowness, 1-genericity, hyperimmune-freeness and computable traceability. This provides a purely computational semantics for IPC.

- Rutger Kuyper
- Math. Log. Q.
- 2014

We consider the complexity of satisfiability in ε-logic, a probability logic. We show that for the relational fragment this problem is Σ 1 1-complete for rational ε ∈ (0, 1), answering a question by Terwijn. In contrast, we show that satisfiability in 0-logic is decidable. The methods we employ to prove this fact also allow us to show that 0-logic is… (More)

- Uri Andrews, Rutger Kuyper, Steffen Lempp, Mariya Ivanova Soskova, Mars M. Yamaleev
- Computability and Complexity
- 2017

- Rutger Kuyper
- Studia Logica
- 2015

Kolmogorov introduced an informal calculus of problems in an attempt to provide a classical semantics for intuitionistic logic. This was later formalised by Medvedev and Muchnik as what has come to be called the Medvedev and Muchnik lattices. However, they only formalised this for propositional logic, while Kolmogorov also discussed the universal… (More)

- Laurent Bienvenu, Rutger Kuyper
- Computability and Complexity
- 2017