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29Hans-Dieter Donder and Peter Koepke. On the consistency strength of ‘accessible’ Jonsson cardinals and of the weak Chang conjecture. Annals of pure and applied logic, vol. 25 , pp. 233–261. - Peter Koepke. Some applications of short core models. Annals of pure and applied logic, vol. 37 , pp. 179–204 (review)Journal of Symbolic Logic 54 (4): 1496-1497. 1989.
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2James E. Baumgartner. On the size of closed unbounded sets. Annals of pure and applied logic, vol. 54 , pp. 195–227 (review)Bulletin of Symbolic Logic 7 (4): 538-539. 2001.
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22Classification theory and 0#Journal of Symbolic Logic 68 (2): 580-588. 2003.We characterize the classifiability of a countable first-order theory T in terms of the solvability of the potential-isomorphism problem for models of T.
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24The tree property at the double successor of a singular cardinal with a larger gapAnnals of Pure and Applied Logic 169 (6): 548-564. 2018.
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20On strong forms of reflection in set theoryMathematical Logic Quarterly 62 (1-2): 52-58. 2016.In this paper we review the most common forms of reflection and introduce a new form which we call sharp‐generated reflection. We argue that sharp‐generated reflection is the strongest form of reflection which can be regarded as a natural generalization of the Lévy reflection theorem. As an application we formulate the principle sharp‐maximality with the corresponding hypothesis. The statement is an analogue of the (Inner Model Hypothesis, introduced in ) which is compatible with the existence o…Read more
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31A null ideal for inaccessiblesArchive for Mathematical Logic 56 (5-6): 691-697. 2017.In this paper we introduce a tree-like forcing notion extending some properties of the random forcing in the context of 2κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^\kappa $$\end{document}, κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usep…Read more
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17Analytic equivalence relations and bi-embeddabilityJournal of Symbolic Logic 76 (1): 243-266. 2011.Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This is in strong contrast to the case of the isomorphism relation, which as an equivalence relation on graphs is far from complete.In this article we strengthen the results of [5] by showing that not only does bi-embeddability give rise to analytic equivalence rela…Read more
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4Annual Meeting of the Association for Symbolic Logic, Durham, 1992Journal of Symbolic Logic 58 (1): 370-382. 1993.
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32Regularity properties on the generalized realsAnnals of Pure and Applied Logic 167 (4): 408-430. 2016.
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28Cichoń’s diagram, regularity properties and $${\varvec{\Delta}^1_3}$$ Δ 3 1 sets of realsArchive for Mathematical Logic 53 (5-6): 695-729. 2014.We study regularity properties related to Cohen, random, Laver, Miller and Sacks forcing, for sets of real numbers on the Δ31\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Delta}^1_3}$$\end{document} level of the projective hieararchy. For Δ21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{w…Read more
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9The completeness of isomorphismIn Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies, De Gruyter. pp. 157-164. 2014.
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161996–97 Annual Meeting of the Association for Symbolic LogicBulletin of Symbolic Logic 3 (3): 378-396. 1997.
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19A simpler proof of Jensen's coding theoremAnnals of Pure and Applied Logic 70 (1): 1-16. 1994.Jensen's remarkable Coding Theorem asserts that the universe can be included in L[R] for some real R, via class forcing. The purpose of this article is to present a simpler proof of Jensen's theorem, obtained by implementing some changes first developed for the theory of Strong Coding. In particular, our proof avoids the split into cases, according to whether or not 0# exists in the ground model
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18Δ1-DefinabilityAnnals of Pure and Applied Logic 89 (1): 93-99. 1997.We isolate a condition on a class A of ordinals sufficient to Δ1-code it by a real in a class-generic extension of L. We then apply this condition to show that the class of ordinals of L-cofinality ω is Δ1 in a real of L-degree strictly below O#
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58Cardinal characteristics and projective wellordersAnnals of Pure and Applied Logic 161 (7): 916-922. 2010.Using countable support iterations of S-proper posets, we show that the existence of a definable wellorder of the reals is consistent with each of the following: , and
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51Cardinal characteristics, projective wellorders and large continuumAnnals of Pure and Applied Logic 164 (7-8): 763-770. 2013.We extend the work of Fischer et al. [6] by presenting a method for controlling cardinal characteristics in the presence of a projective wellorder and 2ℵ0>ℵ2. This also answers a question of Harrington [9] by showing that the existence of a Δ31 wellorder of the reals is consistent with Martinʼs axiom and 2ℵ0=ℵ3
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10Definability degreesMathematical Logic Quarterly 51 (5): 448-449. 2005.We establish the equiconsistency of a simple statement in definability theory with the failure of the GCH at all infinite cardinals. The latter was shown by Foreman and Woodin to be consistent, relative to the existence of large cardinals
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61Co-analytic mad families and definable wellordersArchive for Mathematical Logic 52 (7-8): 809-822. 2013.We show that the existence of a ${\Pi^1_1}$ -definable mad family is consistent with the existence of a ${\Delta^{1}_{3}}$ -definable well-order of the reals and ${\mathfrak{b}=\mathfrak{c}=\aleph_3}$
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27Review: Donald A. Martin, A. S. Kechris, D. A. Martin, Y. N. Moschovakis, The Largest Countable this, that, and the other; Alexander S. Kechris, Donald A. Martin, Robert M. Solovay, Introduction to $Q$-Theory; Steve Jackson, A. S. Kechris, D. A. Martin, J. R. Steel, AD and the Projective Ordinals (review)Journal of Symbolic Logic 57 (1): 262-264. 1992.
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17Review: James E. Baumgartner, On the Size of Closed Unbounded Sets (review)Bulletin of Symbolic Logic 7 (4): 538-539. 2001.