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  1. Deirdre Haskell Denis Hirschfeldt Andre Scedrov & Ralf Schindler (forthcoming). Full-Text of Current Issues of The Bulletin of Symbolic Logic and The Journal of Symbolic Logic is Available to All ASL Members Electronically Via Project Euclid. Individual Members Who Wish to Gain Access Should Follow These Instructions: 11) Go to Http://Projecteuclid. Org:(2) in The'for Subscribers" Tab. Click on" Log in for Existing Subscribers':(3) Click on" Create a Profile Here" in the Center of the Login Page:(4) Till in at Least the Required Fields. [REVIEW] Bulletin of Symbolic Logic.
     
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  2. Benjamin Claverie & Ralf Schindler (2012). Woodin's Axiom (*), Bounded Forcing Axioms, and Precipitous Ideals on Ω₁. Journal of Symbolic Logic 77 (2):475-498.
    If the Bounded Proper Forcing Axiom BPFA holds, then Mouse Reflection holds at N₂ with respect to all mouse operators up to the level of Woodin cardinals in the next ZFC-model. This yields that if Woodin's ℙ max axiom (*) holds, then BPFA implies that V is closed under the "Woodin-in-the-next-ZFC-model" operator. We also discuss stronger Mouse Reflection principles which we show to follow from strengthenings of BPFA, and we discuss the theory BPFA plus "NS ω1 is precipitous" and strengthenings (...)
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  3. Ralf Schindler & Philipp Schlicht (2011). Thin Equivalence Relations in Scaled Pointclasses. Mathematical Logic Quarterly 57 (6):615-620.
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  4. Gunter Fuchs, Itay Neeman & Ralf Schindler (2010). A Criterion for Coarse Iterability. Archive for Mathematical Logic 49 (4):447-467.
    The main result of this paper is the following theorem: Let M be a premouse with a top extender, F. Suppose that (a) M is linearly coarsely iterable via hitting F and its images, and (b) if M * is a linear iterate of M as in (a), then M * is coarsely iterable with respect to iteration trees which do not use the top extender of M * and its images. Then M is coarsely iterable.
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  5. Daniel Busche & Ralf Schindler (2009). The Strength of Choiceless Patterns of Singular and Weakly Compact Cardinals. Annals of Pure and Applied Logic 159 (1):198-248.
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  6. Benjamin Claverie & Ralf Schindler (2009). Increasing U 2 by a Stationary Set Preserving Forcing. Journal of Symbolic Logic 74 (1):187-200.
    We show that if I is a precipitous ideal on ω₁ and if θ > ω₁ is a regular cardinal, then there is a forcing P = P(I, θ) which preserves the stationarity of all I-positive sets such that in $V^P $ , is a generic iterate of a countable structure . This shows that if the nonstationary ideal on ω₁ is precipitous and $H_\theta ^\# $ exists, then there is a stationary set preserving forcing which increases $\delta _2^1 $ (...)
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  7. Ronald Jensen, Ernest Schimmerling, Ralf Schindler & John Steel (2009). Stacking Mice. Journal of Symbolic Logic 74 (1):315-335.
    We show that either of the following hypotheses imply that there is an inner model with a proper class of strong cardinals and a proper class of Woodin cardinals. 1) There is a countably closed cardinal k ≥ N₃ such that □k and □(k) fail. 2) There is a cardinal k such that k is weakly compact in the generic extension by Col(k, k⁺). Of special interest is 1) with k = N₃ since it follows from PFA by theorems of (...)
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  8. Ralf Schindler (2009). U. Blau, Die Logik der Unbestimmtheiten und Paradoxien. Bulletin of Symbolic Logic 35 (4).
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  9. Ralf Schindler & John Steel (2009). The Self-Iterability of L[E]. Journal of Symbolic Logic 74 (3):751-779.
    Let L[E] be an iterable tame extender model. We analyze to which extent L[E] knows fragments of its own iteration strategy. Specifically, we prove that inside L[E], for every cardinal K which is not a limit of Woodin cardinals there is some cutpoint t K > a>ω1 are cardinals, then ◊$_{K.\lambda }^* $ holds true, and if in addition λ is regular, then ◊$_{K.\lambda }^* $ holds true.
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  10. Andrés Eduardo Caicedo & Ralf Schindler (2006). Projective Well-Orderings of the Reals. Archive for Mathematical Logic 45 (7):783-793.
    If there is no inner model with ω many strong cardinals, then there is a set forcing extension of the universe with a projective well-ordering of the reals.
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  11. Deirdre Haskell Denis Hirschfeldt, Andre Scedrov & Ralf Schindler (2006). Full-Text of Current Issues of The Bulletin of Symbolic Logic and The Journal of Symbolic Logic is Available to All ASL Members Electronically Via Project Euclid. Individual Members Who Wish to Gain Access Should Follow These Instructions:(1) Go to Http://Projecteuclid. Org:(2) in the" for Subscribers' Tab. Click on'Log in for Existing Subscribers':(3) Click on" Create a Profile Here" in the Center of the Login Page:(4) Fill in at Least the Required Fields. [REVIEW] Bulletin of Symbolic Logic 12 (2):362.
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  12. Peter Koepke & Ralf Schindler (2006). Homogeneously Souslin Sets in Small Inner Models. Archive for Mathematical Logic 45 (1):53-61.
    We prove that every homogeneously Souslin set is coanalytic provided that either (a) 0long does not exist, or else (b) V = K, where K is the core model below a μ-measurable cardinal.
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  13. Ralf Schindler (2006). Core Models in the Presence of Woodin Cardinals. Journal of Symbolic Logic 71 (4):1145 - 1154.
    Let 0 < n < ω. If there are n Woodin cardinals and a measurable cardinal above, but $M_{n+1}^{\#}$ doesn't exist, then the core model K exists in a sense made precise. An Iterability Inheritance Hypothesis is isolated which is shown to imply an optimal correctness result for K.
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  14. Ralf Schindler (2006). Iterates of the Core Model. Journal of Symbolic Logic 71 (1):241 - 251.
    Let N be a transitive model of ZFC such that ωN ⊂ N and P(R) ⊂ N. Assume that both V and N satisfy "the core model K exists." Then KN is an iterate of K. i.e., there exists an iteration tree J on K such that J has successor length and $\mathit{M}_{\infty}^{\mathit{J}}=K^{N}$. Moreover, if there exists an elementary embedding π: V → N then the iteration map associated to the main branch of J equals π ↾ K. (This answers (...)
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  15. Thoralf Räsch & Ralf Schindler (2005). A New Condensation Principle. Archive for Mathematical Logic 44 (2):159-166.
    We generalize ∇(A), which was introduced in [Sch∞], to larger cardinals. For a regular cardinal κ>ℵ0 we denote by ∇ κ (A) the statement that and for all regular θ>κ, is stationary in It was shown in [Sch∞] that can hold in a set-generic extension of L. We here prove that can hold in a set-generic extension of L as well. In both cases we in fact get equiconsistency theorems. This strengthens results of [Rä00] and [Rä01]. is equivalent with the (...)
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  16. William Mitchell & Ralf Schindler (2004). A Universal Extender Model Without Large Cardinals in V. Journal of Symbolic Logic 69 (2):371 - 386.
    We construct, assuming that there is no inner model with a Woodin cardinal but without any large cardinal assumption, a model $K^{c}$ which is iterable for set length iterations, which is universal with respect to all weasels with which it can be compared, and (assuming GCH) is universal with respect to set sized premice.
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  17. Ralf Schindler (2004). NCA Da Costa and FA Doria. Consequences of an Exotic Definition for P= NP. Applied Mathematics and Computation, Vol. 145 (2003), Pp. 655–665. [REVIEW] Bulletin of Symbolic Logic 10 (1):118-119.
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  18. Sy D. Friedman & Ralf Schindler (2003). Universally Baire Sets and Definable Well-Orderings of the Reals. Journal of Symbolic Logic 68 (4):1065-1081.
    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.
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  19. Ralf-Dieter Schindler (2002). The Core Model for Almost Linear Iterations. Annals of Pure and Applied Logic 116 (1-3):205-272.
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  20. Ralf-Dieter Schindler, John Steel & Martin Zeman (2002). Deconstructing Inner Model Theory. Journal of Symbolic Logic 67 (2):721-736.
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  21. Matthew Foreman, Menachem Magidor & Ralf-Dieter Schindler (2001). The Consistency Strength of Successive Cardinals with the Tree Property. 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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  22. Ralf-Dieter Schindler (2001). Proper Forcing and Remarkable Cardinals II. 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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  23. Kai Hauser & Ralf-Dieter Schindler (2000). Projective Uniformization Revisited. Annals of Pure and Applied Logic 103 (1-3):109-153.
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  24. Ralf-Dieter Schindler (2000). Proper Forcing and Remarkable Cardinals. Bulletin of Symbolic Logic 6 (2):176-184.
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  25. Ralf-Dieter Schindler (1999). Strong Cardinals and Sets of Reals in Lω1(ℝ). Mathematical Logic Quarterly 45 (3):361-369.
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  26. Ralf-Dieter Schindler (1999). Successive Weakly Compact or Singular Cardinals. 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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  27. Ralf-Dieter Schindler (1999). Weak Covering and the Tree Property. 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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  28. Ralf-Dieter Schindler (1998). On a Chang Conjecture. II. 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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  29. Ralf ‐ Dieter Schindler (1997). Weak Covering at Large Cardinals. Mathematical Logic Quarterly 43 (1):22-28.
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  30. Ralf‐Dieter Schindler (1997). Weak Covering at Large Cardinals. Mathematical Logic Quarterly 43 (1):22-28.
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  31. Ralf-Dieter Schindler (1994). A Dilemma in the Philosophy of Set Theory. 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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  32. Ralf-Dieter Schindler (1993). Prädikative Klassen. 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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