15 found
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  1.  15
    Deconstructing Inner Model Theory.Ralf-Dieter Schindler, John Steel & Martin Zeman - 2002 - Journal of Symbolic Logic 67 (2):721-736.
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  2.  6
    Proper Forcing and Remarkable Cardinals II.Ralf-Dieter Schindler - 2001 - Journal of Symbolic Logic 66 (3):1481-1492.
    The current paper proves the results announced in [5]. We isolate a new large cardinal concept, "remarkability." Consistencywise, remarkable cardinals are between ineffable and ω-Erdos cardinals. They are characterized by the existence of "O # -like" embeddings; however, they relativize down to L. It turns out that the existence of a remarkable cardinal is equiconsistent with L(R) absoluteness for proper forcings. In particular, said absoluteness does not imply Π 1 1 determinacy.
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  3.  38
    Proper Forcing and Remarkable Cardinals.Ralf-Dieter Schindler - 2000 - Bulletin of Symbolic Logic 6 (2):176-184.
  4.  5
    Projective Uniformization Revisited.Kai Hauser & Ralf-Dieter Schindler - 2000 - Annals of Pure and Applied Logic 103 (1-3):109-153.
    We give an optimal lower bound in terms of large cardinal axioms for the logical strength of projective uniformization in conjuction with other regularity properties of projective sets of real numbers, namely Lebesgue measurability and its dual in the sense of category . Our proof uses a projective computation of the real numbers which code inital segments of a core model and answers a question in Hauser.
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  5.  5
    The Core Model for Almost Linear Iterations.Ralf-Dieter Schindler - 2002 - Annals of Pure and Applied Logic 116 (1-3):205-272.
    We introduce 0• as a sharp for an inner model with a proper class of strong cardinals. We prove the existence of the core model K in the theory “ does not exist”. Combined with work of Woodin, Steel, and earlier work of the author, this provides the last step for determining the exact consistency strength of the assumption in the statement of the 12th Delfino problem pp. 221–224)).
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  6.  16
    The Consistency Strength of Successive Cardinals with the Tree Property.Matthew Foreman, Menachem Magidor & Ralf-Dieter Schindler - 2001 - Journal of Symbolic Logic 66 (4):1837-1847.
    If ω n has the tree property for all $2 \leq n and $2^{ , then for all X ∈ H ℵ ω and $n exists.
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  7.  9
    Weak Covering and the Tree Property.Ralf-Dieter Schindler - 1999 - Archive for Mathematical Logic 38 (8):515-520.
    Suppose that there is no transitive model of ZFC + there is a strong cardinal, and let K denote the core model. It is shown that if $\delta$ has the tree property then $\delta^{+K} = \delta^+$ and $\delta$ is weakly compact in K.
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  8.  17
    Successive Weakly Compact or Singular Cardinals.Ralf-Dieter Schindler - 1999 - Journal of Symbolic Logic 64 (1):139-146.
    It is shown in ZF that if $\delta are such that δ and δ + are either both weakly compact or singular cardinals and Ω is large enough for putting the core model apparatus into action then there is an inner model with a Woodin cardinal.
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  9.  3
    Strong Cardinals and Sets of Reals in Lω1.Ralf-Dieter Schindler - 1999 - Mathematical Logic Quarterly 45 (3):361-369.
    We generalize results of [3] and [1] to hyperprojective sets of reals, viz. to more than finitely many strong cardinals being involved. We show, for example, that if every set of reals in Lω is weakly homogeneously Souslin, then there is an inner model with an inaccessible limit of strong cardinals.
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  10.  6
    On a Chang Conjecture. II.Ralf-Dieter Schindler - 1998 - Archive for Mathematical Logic 37 (4):215-220.
    Continuing [7], we here prove that the Chang Conjecture $(\aleph_3,\aleph_2) \Rightarrow (\aleph_2,\aleph_1)$ together with the Continuum Hypothesis, $2^{\aleph_0} = \aleph_1$ , implies that there is an inner model in which the Mitchell ordering is $\geq \kappa^{+\omega}$ for some ordinal $\kappa$.
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  11.  7
    The Consistency Strength of Successive Cardinals with the Tree Property.Matthew Foreman, Menachem Magidor & Ralf-Dieter Schindler - 2001 - Journal of Symbolic Logic 66 (4):1837-1847.
    If $\omega_n$ has the tree property for all $2 \leq n < \omega$ and $2^{<\aleph_{\omega}} = \aleph_{\omega}$, then for all $X \in H_{\aleph_{\omega}}$ and $n < \omega, M^#_n$ exists.
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  12.  17
    Prädikative Klassen.Ralf-Dieter Schindler - 1993 - Erkenntnis 39 (2):209 - 241.
    We consider certain predicative classes with respect to their bearing on set theory, namely on its semantics, and on its ontological power. On the one hand, our predicative classes will turn out to be perfectly suited for establishing a nice hierarchy of metalanguages starting from the usual set theoretical language. On the other hand, these classes will be seen to be fairly inappropriate for the formulation of strong principles of infinity. The motivation for considering this very type of classes is (...)
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  13.  2
    Successive Weakly Compact or Singular Cardinals.Ralf-Dieter Schindler - 1999 - Journal of Symbolic Logic 64 (1):139-146.
    It is shown in ZF that if $\delta < \delta^+ < \Omega$ are such that $\delta$ and $\delta^+$ are either both weakly compact or singular cardinals and $\Omega$ is large enough for putting the core model apparatus into action then there is an inner model with a Woodin cardinal.
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  14.  7
    A Dilemma in the Philosophy of Set Theory.Ralf-Dieter Schindler - 1994 - Notre Dame Journal of Formal Logic 35 (3):458-463.
    We show that the following conjecture about the universe V of all sets is wrong: for all set-theoretical (i.e., first order) schemata true in V there is a transitive set "reflecting" in such a way that the second order statement corresponding to is true in . More generally, we indicate the ontological commitments of any theory that exploits reflection principles in order to yield large cardinals. The disappointing conclusion will be that our only apparently good arguments for the existence of (...)
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  15.  1
    Proper Forcing and Remarkable Cardinals II.Ralf-Dieter Schindler - 2001 - Journal of Symbolic Logic 66 (3):1481-1492.
    The current paper proves the results announced in [5]. We isolate a new large cardinal concept, "remarkability." Consistencywise, remarkable cardinals are between ineffable and $\omega$-Erdos cardinals. They are characterized by the existence of "O$^#$-like" embeddings; however, they relativize down to L. It turns out that the existence of a remarkable cardinal is equiconsistent with L absoluteness for proper forcings. In particular, said absoluteness does not imply $\Pi^1_1$ determinacy.
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