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Paul B. Larson [14]Paul Larson [14]
  1. Tetsuya Ishiu & Paul B. Larson (2012). ℛ Max Variations for Separating Club Guessing Principles. Journal of Symbolic Logic 77 (2):532-544.
    In his book on P max [7], Woodin presents a collection of partial orders whose extensions satisfy strong club guessing principles on ω | . In this paper we employ one of the techniques from this book to produce P max variations which separate various club guessing principles. The principle (+) and its variants are weak guessing principles which were first considered by the second author [4] while studying games of length ω | . It was shown in [1] that (...)
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  2. Tetsuya Ishiu & Paul B. Larson (2012). Some Results About (+) Proved by Iterated Forcing. Journal of Symbolic Logic 77 (2):515-531.
    We shall show the consistency of CH+ᄀ(+) and CH+(+)+ there are no club guessing sequences on ω₁. We shall also prove that ◊⁺ does not imply the existence of a strong club guessing sequence ω₁.
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  3. Richard Ketchersid, Paul B. Larson & Jindřich Zapletal (2010). Regular Embeddings of the Stationary Tower and Woodin's Σ 2 2 Maximality Theorem. Journal of Symbolic Logic 75 (2):711-727.
    We present Woodin's proof that if there exists a measurable Woodin cardinal δ, then there is a forcing extension satisfying all $\Sigma _{2}^{2}$ sentences ϕ such that CH + ϕ holds in a forcing extension of V by a partial order in V δ . We also use some of the techniques from this proof to show that if there exists a stationary limit of stationary limits of Woodin cardinals, then in a homogeneous forcing extension there is an elementary embedding (...)
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  4. Paul B. Larson (2009). The Filter Dichotomy and Medial Limits. Journal of Mathematical Logic 9 (02):159-165.
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  5. Paul Larson & Saharon Shelah (2009). Splitting Stationary Sets From Weak Forms of Choice. Mathematical Logic Quarterly 55 (3):299-306.
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  6. Paul B. Larson (2008). Martin's Maximum and Definability in H (ℵ2). Annals of Pure and Applied Logic 156 (1):110-122.
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  7. Paul B. Larson & Saharon Shelah (2008). The Stationary Set Splitting Game. Mathematical Logic Quarterly 54 (2):187-193.
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  8. Richard Ketchersid, Paul Larson & Jindřich Zapletal (2007). Increasing $\Delta _{2}^{1}$ and Namba-Style Forcing. Journal of Symbolic Logic 72 (4):1372 - 1378.
    We isolate a forcing which increases the value of $\delta _{2}^{1}$ while preserving ω₁ under the assumption that there is a precipitous ideal on ω₁ and a measurable cardinal.
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  9. Richard Ketchersid, Paul Larson & Jindřich Zapletal (2007). Increasing Δ 1 2 and Namba-Style Forcing. Journal of Symbolic Logic 72 (4):1372-1378.
    We isolate a forcing which increases the value of δ12 while preserving ω₁ under the assumption that there is a precipitous ideal on ω₁ and a measurable cardinal.
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  10. Paul B. Larson (2007). The Nonstationary Ideal in the Pmax Extension. Journal of Symbolic Logic 72 (1):138 - 158.
    The forcing construction Pmax, invented by W. Hugh Woodin, produces a model whose collection of subsets of ω₁ is in some sense maximal. In this paper we study the Boolean algebra induced by the nonstationary ideal on ω₁ in this model. Among other things we show that the induced quotient does not have a simply definable form. We also prove several results about saturation properties of the ideal in this extension.
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  11. Lúcia R. Junqueira, Paul Larson & Franklin D. Tall (2006). Compact Spaces, Elementary Submodels, and the Countable Chain Condition. Annals of Pure and Applied Logic 144 (1):107-116.
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  12. Paul Larson (2005). Saturation, Suslin Trees and Meager Sets. Archive for Mathematical Logic 44 (5):581-595.
    We show, using a variation of Woodin’s partial order ℙ max , that it is possible to destroy the saturation of the nonstationary ideal on ω 1 by forcing with a Suslin tree. On the other hand, Suslin trees typcially preserve saturation in extensions by ℙ max variations where one does not try to arrange it otherwise. In the last section, we show that it is possible to have a nonmeager set of reals of size ℵ1, saturation of the nonstationary (...)
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  13. Paul B. Larson (2005). Neeman Itay. Games of Countable Length. Sets and Proofs (Leeds, 1997), Edited by Cooper S. Barry and Truss John K., London Mathematical Society Lecture Note Series, Vol. 258. Cambridge University Press, Cambridge, 1999, Pp. 159-196. Neeman Itay. Unraveling Π1 1 Sets. Annals of Pure and Applied Logic, Vol. 106, No. 1–3 (2000), Pp. 151-205. Neeman Itay. Unraveling Π1 1 Sets, Revisited. Israel Journal of Mathematics, to Appear. [REVIEW] Bulletin of Symbolic Logic 11 (4):542-544.
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  14. Paul B. Larson (2005). The Canonical Function Game. Archive for Mathematical Logic 44 (7):817-827.
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  15. I. Neeman & Paul B. Larson (2005). REVIEWS-Three Papers. Bulletin of Symbolic Logic 11 (4):542-544.
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  16. Paul Larson & Saharon Shelah (2003). Bounding by Canonical Functions, with Ch. Journal of Mathematical Logic 3 (02):193-215.
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  17. Paul Larson (2002). A Uniqueness Theorem for Iterations. Journal of Symbolic Logic 67 (4):1344-1350.
    If M is a countable transitive model of $ZFC+MA_{\aleph_{1}}$ , then for every real x there is a unique shortest iteration $j: M \rightarrow N$ with $x \in N$ , or none at all.
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  18. Paul B. Larson (2002). Neeman Itay and Zapletal Jindřich. Proper Forcings and Absoluteness in L (ℝ). Commentationes Mathematicae Universitatis Carolinae, Vol. 39 (1998), Pp. 281–301. Neeman Itay and Zapletal Jindřich. Proper Forcing and L (ℝ). The Journal of Symbolic Logic, Vol. 66 (2001), Pp. 801–810. [REVIEW] Bulletin of Symbolic Logic 8 (4):548-550.
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  19. Paul B. Larson (2002). Review: Itay Neeman, Jind?Ich Zapletal, Proper Forcings and Absoluteness in $L({Bbb R})$; Itay Neeman, Jind?Ich Zapletal, Proper Forcing and $L({Bbb R})$. [REVIEW] Bulletin of Symbolic Logic 8 (4):548-550.
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  20. Paul B. Larson (2002). Review: W. Hugh Woodin, The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal. [REVIEW] Bulletin of Symbolic Logic 8 (1):91-93.
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  21. I. Neeman, J. Zapletal & Paul B. Larson (2002). REVIEWS-Two Papers-Proper Forcing and L (R). Bulletin of Symbolic Logic 8 (4):548-549.
     
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  22. Paul Larson (2000). Martin's Maximum and The. Annals of Pure and Applied Logic 106 (1-3):135-149.
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  23. Paul Larson (2000). Martin's Maximum and the Pmaxaxiom (∗). Annals of Pure and Applied Logic 106 (1):135-149.
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  24. Paul Larson (2000). Separating Stationary Reflection Principles. Journal of Symbolic Logic 65 (1):247-258.
    We present a variety of (ω 1 ,∞)-distributive forcings which when applied to models of Martin's Maximum separate certain well known reflection principles. In particular, we do this for the reflection principles SR, SR α (α ≤ ω 1 ), and SRP.
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  25. Paul Larson (2000). The Size of $Tilde{T}$. Archive for Mathematical Logic 39 (7):541-568.
    Given a stationary subset T of $\omega_{1}$ , let $\tilde{T}$ be the set of ordinals in the interval $(\omega_{1}, \omega_{2})$ which are necessarily in the image of T by any embedding derived from the nonstationary ideal. We consider the question of the size of $\tilde{T}$ , givenT, and use Martin's Maximum and $\mathbb{P}_{max}$ to give some answers.
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  26. Paul Larson (2000). The Size of [Mathematical Formula]. Archive for Mathematical Logic 7.
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  27. Paul Larson (1999). An $Mathbb{S}_{Max}$ Variation for One Souslin Tree. Journal of Symbolic Logic 64 (1):81-98.
    We present a variation of the forcing $\mathbb{S}_{max}$ as presented in Woodin [4]. Our forcing is a $\mathbb{P}_{max}$-style construction where each model condition selects one Souslin tree. In the extension there is a Souslin tree T$_G$ which is the direct limit of the selected Souslin trees in the models of the generic. In some sense, the generic extension is a maximal model of "there exists a minimal Souslin tree," with T$_G$ being this minimal tree. In particular, in the extension this (...)
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  28. Paul Larson (1999). An Smax Variation for One Souslin Tree. Journal of Symbolic Logic 64 (1):81 - 98.
    We present a variation of the forcing S max as presented in Woodin [4]. Our forcing is a P max -style construction where each model condition selects one Souslin tree. In the extension there is a Souslin tree T G which is the direct limit of the selected Souslin trees in the models of the generic. In some sense, the generic extension is a maximal model of "there exists a minimal Souslin tree," with T G being this minimal tree. In (...)
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