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70Downey, R., Gasarch, W. and Moses, M., The structureAnnals of Pure and Applied Logic 70 (1): 287. 1994.
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122Hans-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. 179–204Journal of Symbolic Logic 54 (4): 1496-1497. 1989.
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135Classification 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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59The 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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90On 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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62A 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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44Annual Meeting of the Association for Symbolic Logic, Durham, 1992Journal of Symbolic Logic 58 (1): 370-382. 1993.
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95Regularity properties on the generalized realsAnnals of Pure and Applied Logic 167 (4): 408-430. 2016.
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69Cichoń’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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841996–97 Annual Meeting of the Association for Symbolic LogicBulletin of Symbolic Logic 3 (3): 378-396. 1997.
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67A 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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93Δ1-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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151Cardinal 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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149Cardinal 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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56Definability 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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125Co-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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152Projective wellorders and mad families with large continuumAnnals of Pure and Applied Logic 162 (11): 853-862. 2011.We show that is consistent with the existence of a -definable wellorder of the reals and a -definable ω-mad subfamily of [ω]ω
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91
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132Jensen's Σ* theory and the combinatorial content of V = LJournal of Symbolic Logic 59 (3). 1994.
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129Universally baire sets and definable well-orderings of the realsJournal of Symbolic Logic 68 (4): 1065-1081. 2003.Let n ≥ 3 be an integer. We show that it is consistent (relative to the consistency of n - 2 strong cardinals) that every $\Sigma_n^1-set$ of reals is universally Baire yet there is a (lightface) projective well-ordering of the reals. The proof uses "David's trick" in the presence of inner models with strong cardinals
