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  1.  12
    The Exact Strength of the Class Forcing Theorem.Victoria Gitman, Joel David Hamkins, Peter Holy, Philipp Schlicht & Kameryn J. Williams - 2020 - Journal of Symbolic Logic 85 (3):869-905.
    The class forcing theorem, which asserts that every class forcing notion ${\mathbb {P}}$ admits a forcing relation $\Vdash _{\mathbb {P}}$, that is, a relation satisfying the forcing relation recursion—it follows that statements true in the corresponding forcing extensions are forced and forced statements are true—is equivalent over Gödel–Bernays set theory $\text {GBC}$ to the principle of elementary transfinite recursion $\text {ETR}_{\text {Ord}}$ for class recursions of length $\text {Ord}$. It is also equivalent to the existence of truth predicates for the (...)
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  2.  15
    Characterizations of Pretameness and the Ord-Cc.Peter Holy, Regula Krapf & Philipp Schlicht - 2018 - Annals of Pure and Applied Logic 169 (8):775-802.
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  3.  5
    Small Models, Large Cardinals, and Induced Ideals.Peter Holy & Philipp Lücke - 2021 - Annals of Pure and Applied Logic 172 (2):102889.
    We show that many large cardinal notions up to measurability can be characterized through the existence of certain filters for small models of set theory. This correspondence will allow us to obtain a canonical way in which to assign ideals to many large cardinal notions. This assignment coincides with classical large cardinal ideals whenever such ideals had been defined before. Moreover, in many important cases, relations between these ideals reflect the ordering of the corresponding large cardinal properties both under direct (...)
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  4.  9
    Small Embedding Characterizations for Large Cardinals.Peter Holy, Philipp Lücke & Ana Njegomir - 2019 - Annals of Pure and Applied Logic 170 (2):251-271.
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  5.  25
    Forcing Lightface Definable Well-Orders Without the GCH.David Asperó, Peter Holy & Philipp Lücke - 2015 - Annals of Pure and Applied Logic 166 (5):553-582.
  6.  2
    An Axiomatic Approach to Forcing in a General Setting.Rodrigo A. Freire & Peter Holy - forthcoming - Bulletin of Symbolic Logic:1-21.
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  7.  3
    Ideal Topologies in Higher Descriptive Set Theory.Peter Holy, Marlene Koelbing, Philipp Schlicht & Wolfgang Wohofsky - 2022 - Annals of Pure and Applied Logic 173 (4):103061.
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  8.  16
    Large Cardinals and Lightface Definable Well-Orders, Without the Gch.Sy-David Friedman, Peter Holy & Philipp Lücke - 2015 - Journal of Symbolic Logic 80 (1):251-284.
  9.  14
    Local Club Condensation and L-Likeness.Peter Holy, Philip Welch & Liuzhen Wu - 2015 - Journal of Symbolic Logic 80 (4):1361-1378.
  10.  9
    Σ1-Wellorders Without Collapsing.Peter Holy - 2015 - Archive for Mathematical Logic 54 (3-4):453-462.
    Given an uncountable cardinal κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa}$$\end{document} that satisfies κκ=κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa^{\kappa}=\kappa}$$\end{document}, we provide a forcing that is <κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${<\kappa}$$\end{document} -closed, has size 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} and is κ+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa^+}$$\end{document} -cc, to introduce a Σ1-definable wellorder of H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...)
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