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  1. Rutger Kuyper & Sebastiaan A. Terwijn (2013). Model Theory of Measure Spaces and Probability Logic. Review of Symbolic Logic 6 (3):367-393.
    We study the model-theoretic aspects of a probability logic suited for talking about measure spaces. This nonclassical logic has a model theory rather different from that of classical predicate logic. In general, not every satisfiable set of sentences has a countable model, but we show that one can always build a model on the unit interval. Also, the probability logic under consideration is not compact. However, using ultraproducts we can prove a compactness theorem for a certain class of weak models.
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  2. Andrea Sorbi & Sebastiaan A. Terwijn (2008). Intermediate Logics and Factors of the Medvedev Lattice. Annals of Pure and Applied Logic 155 (2):69-85.
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  3. Sebastiaan A. Terwijn (2008). On the Structure of the Medvedev Lattice. Journal of Symbolic Logic 73 (2):543 - 558.
    We investigate the structure of the Medvedev lattice as a partial order. We prove that every interval in the lattice is either finite, in which case it is isomorphic to a finite Boolean algebra, or contains an antichain of size $2^{2^{\aleph }0}$ , the size of the lattice itself. We also prove that it is consistent with ZFC that the lattice has chains of size $2^{2^{\aleph }0}$ , and in fact these big chains occur in every infinite interval. We also (...)
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  4. Sebastiaan A. Terwijn (2007). Kripke Models, Distributive Lattices, and Medvedev Degrees. Studia Logica 85 (3):319 - 332.
    We define a variant of the standard Kripke semantics for intuitionistic logic, motivated by the connection between constructive logic and the Medvedev lattice. We show that while the new semantics is still complete, it gives a simple and direct correspondence between Kripke models and algebraic structures such as factors of the Medvedev lattice.
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  5. Cristian S. Calude, Ludwig Staiger & Sebastiaan A. Terwijn (2006). On Partial Randomness. Annals of Pure and Applied Logic 138 (1):20-30.
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  6. Rod Downey, Denis R. Hirschfeldt, André Nies & Sebastiaan A. Terwijn (2006). Calibrating Randomness. Bulletin of Symbolic Logic 12 (3):411-491.
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  7. Sebastiaan A. Terwijn (2006). Constructive Logic and the Medvedev Lattice. Notre Dame Journal of Formal Logic 47 (1):73-82.
    We study the connection between factors of the Medvedev lattice and constructive logic. The algebraic properties of these factors determine logics lying in between intuitionistic propositional logic and the logic of the weak law of the excluded middle (also known as De Morgan, or Jankov, logic). We discuss the relation between the weak law of the excluded middle and the algebraic notion of join-reducibility. Finally we discuss autoreducible degrees.
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  8. Sebastiaan A. Terwijn (2006). The Medvedev Lattice of Computably Closed Sets. Archive for Mathematical Logic 45 (2):179-190.
    Simpson introduced the lattice of Π0 1 classes under Medvedev reducibility. Questions regarding completeness in are related to questions about measure and randomness. We present a solution to a question of Simpson about Medvedev degrees of Π0 1 classes of positive measure that was independently solved by Simpson and Slaman. We then proceed to discuss connections to constructive logic. In particular we show that the dual of does not allow an implication operator (i.e. that is not a Heyting algebra). We (...)
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  9. André Nies, Frank Stephan & Sebastiaan A. Terwijn (2005). Randomness, Relativization and Turing Degrees. Journal of Symbolic Logic 70 (2):515 - 535.
    We compare various notions of algorithmic randomness. First we consider relativized randomness. A set is n-random if it is Martin-Löf random relative to θ(n−1). We show that a set is 2-random if and only if there is a constant c such that infinitely many initial segments x of the set are c-incompressible: C(x) ≥ |x| − c. The 'only if' direction was obtained independently by Joseph Miller. This characterization can be extended to the case of time-bounded C-complexity. Next we prove (...)
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  10. Sebastiaan A. Terwijn & Domenico Zambella (2001). Computational Randomness and Lowness. Journal of Symbolic Logic 66 (3):1199-1205.
    We prove that there are uncountably many sets that are low for the class of Schnorr random reals. We give a purely recursion theoretic characterization of these sets and show that they all have Turing degree incomparable to 0'. This contrasts with a result of Kučera and Terwijn [5] on sets that are low for the class of Martin-Löf random reals.
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  11. Antonin Kučera & Sebastiaan A. Terwijn (1999). Lowness for the Class of Random Sets. Journal of Symbolic Logic 64 (4):1396-1402.
    A positive answer to a question of M. van Lambalgen and D. Zambella whether there exist nonrecursive sets that are low for the class of random sets is obtained. Here a set A is low for the class RAND of random sets if RAND = RAND A.
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  12. Sebastiaan A. Terwijn & Leen Torenvliet (1998). Arithmetical Measure. Mathematical Logic Quarterly 44 (2):277-286.
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