Switch to: References

Add citations

You must login to add citations.
  1. In Memoriam: James Earl Baumgartner.J. A. Larson - 2017 - Archive for Mathematical Logic 56 (7-8):877-909.
    James Earl Baumgartner came of age mathematically during the emergence of forcing as a fundamental technique of set theory, and his seminal research changed the way set theory is done. He made fundamental contributions to the development of forcing, to our understanding of uncountable orders, to the partition calculus, and to large cardinals and their ideals. He promulgated the use of logic such as absoluteness and elementary submodels to solve problems in set theory, he applied his knowledge of set theory (...)
    No categories
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  • A Non-Implication Between Fragments of Martin’s Axiom Related to a Property Which Comes From Aronszajn Trees.Teruyuki Yorioka - 2010 - Annals of Pure and Applied Logic 161 (4):469-487.
    We introduce a property of forcing notions, called the anti-, which comes from Aronszajn trees. This property canonically defines a new chain condition stronger than the countable chain condition, which is called the property . In this paper, we investigate the property . For example, we show that a forcing notion with the property does not add random reals. We prove that it is consistent that every forcing notion with the property has precaliber 1 and for forcing notions with the (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Combinatorial Properties of the Ideal ℬ2.J. Cichon, A. Roslanowski, J. Steprans & B. Weglorz - 1993 - Journal of Symbolic Logic 58 (1):42-54.
    By B2 we denote the σ-ideal of all subsets A of the Cantor set {0,1}ω such that for every infinite subset T of ω the restriction A∣{0,1}T is a proper subset of {0,1}T. In this paper we investigate set theoretical properties of this and similar ideals.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • A Very Discontinuous Borel Function.Juris Steprāns - 1993 - Journal of Symbolic Logic 58 (4):1268 - 1283.
    It is shown to be consistent that the reals are covered by ℵ1 meagre sets yet there is a Baire class 1 function which cannot be covered by fewer than ℵ2 continuous functions. A new cardinal invariant is introduced which corresponds to the least number of continuous functions required to cover a given function. This is characterized combinatorially. A forcing notion similar to, but not equivalent to, superperfect forcing is introduced.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  • Similar but Not the Same: Various Versions of ♣ Do Not Coincide.Mirna Džamonja & Saharon Shelah - 1999 - Journal of Symbolic Logic 64 (1):180 - 198.
    We consider various versions of the ♣ principle. This principle is a known consequence of $\lozenge$ . It is well known that $\lozenge$ is not sensitive to minor changes in its definition, e.g., changing the guessing requirement form "guessing exactly" to "guessing modulo a finite set". We show however, that this is not true for ♣. We consider some other variants of ♣ as well.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Partition Subalgebras for Maximal Almost Disjoint Families.Alan Dow & Jinyuan Zhou - 2002 - Annals of Pure and Applied Logic 117 (1-3):223-259.
    Partitioner algebras are defined by Baumgartner and Weese 619) as a natural tool for studying the properties of maximal almost disjoint families of subsets of ω. We prove from PFA+ and that there exists a partitioner algebra which contains a subalgebra which is not representable as a partitioner algebra.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  • Proper Forcing, Cardinal Arithmetic, and Uncountable Linear Orders.Justin Tatch Moore - 2005 - Bulletin of Symbolic Logic 11 (1):51-60.
    In this paper I will communicate some new consequences of the Proper Forcing Axiom. First, the Bounded Proper Forcing Axiom implies that there is a well ordering of R which is Σ 1 -definable in (H(ω 2 ), ∈). Second, the Proper Forcing Axiom implies that the class of uncountable linear orders has a five element basis. The elements are X, ω 1 , ω 1 * , C, C * where X is any suborder of the reals of size (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark  
  • Bounded Forcing Axioms and the Continuum.David Asperó & Joan Bagaria - 2001 - Annals of Pure and Applied Logic 109 (3):179-203.
    We show that bounded forcing axioms are consistent with the existence of -gaps and thus do not imply the Open Coloring Axiom. They are also consistent with Jensen's combinatorial principles for L at the level ω2, and therefore with the existence of an ω2-Suslin tree. We also show that the axiom we call BMM3 implies 21=2, as well as a stationary reflection principle which has many of the consequences of Martin's Maximum for objects of size 2. Finally, we give an (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • The Real Line in Elementary Submodels of Set Theory.Kenneth Kunen & Franklin D. Tall - 2000 - Journal of Symbolic Logic 65 (2):683-691.
    Keywords: Elementary Submodel; Real Line; Order-Isomorphic.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  • Fragments of Martin's Axiom and Δ13 Sets of Reals.Joan Bagaria - 1994 - Annals of Pure and Applied Logic 69 (1):1-25.
    We strengthen a result of Harrington and Shelah by showing that, unless ω1 is an inaccessible cardinal in L, a relatively weak fragment of Martin's axiom implies that there exists a δ13 set of reals without the property of Baire.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  • Covering a Function on the Plane by Two Continuous Functions on an Uncountable Square – the Consistency.Mariusz Rabus & Saharon Shelah - 2000 - Annals of Pure and Applied Logic 103 (1-3):229-240.
    It is consistent that for every function there is an uncountable set and two continuous functions such that f {f0, f1} for every A2,α≠β.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Weak Diamond and Open Colorings.Justin Tatch Moore - 2003 - Journal of Mathematical Logic 3 (01):119-125.
  • Extraspecial p-groups.Saharon Shelah & Juris Steprāns - 1987 - Annals of Pure and Applied Logic 34 (1):87-97.
    Direct download (4 more)  
    Translate
     
     
    Export citation  
     
    Bookmark   3 citations  
  • Potential Continuity of Colorings.Stefan Geschke - 2008 - Archive for Mathematical Logic 47 (6):567-578.
    We say that a coloring ${c: [\kappa]^n\to 2}$ is continuous if it is continuous with respect to some second countable topology on κ. A coloring c is potentially continuous if it is continuous in some ${\aleph_1}$ -preserving extension of the set-theoretic universe. Given an arbitrary coloring ${c:[\kappa]^n\to 2}$ , we define a forcing notion ${\mathbb P_c}$ that forces c to be continuous. However, this forcing might collapse cardinals. It turns out that ${\mathbb P_c}$ is c.c.c. if and only if c (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  • Set Theoretical Aspects of the Banach Space L∞/C0.Magdalena Grzech - 2004 - Annals of Pure and Applied Logic 126 (1-3):301-308.
    Relative results concerning the Banach space l ∞ / c 0 are presented. We show that some basic properties of the Banach space l ∞ / c 0 implied by CH and OCA are different.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  • Some Weak Fragments of Martin’s Axiom Related to the Rectangle Refining Property.Teruyuki Yorioka - 2008 - Archive for Mathematical Logic 47 (1):79-90.
    We introduce the anti-rectangle refining property for forcing notions and investigate fragments of Martin’s axiom for ℵ1 dense sets related to the anti-rectangle refining property, which is close to some fragment of Martin’s axiom for ℵ1 dense sets related to the rectangle refining property, and prove that they are really weaker fragments.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Continuous Ramsey Theory on Polish Spaces and Covering the Plane by Functions.Stefan Geschke, Martin Goldstern & Menachem Kojman - 2004 - Journal of Mathematical Logic 4 (2):109-145.
  • Combinatorial Dichotomies in Set Theory.Stevo Todorcevic - 2011 - Bulletin of Symbolic Logic 17 (1):1-72.
    We give an overview of a research line concentrated on finding to which extent compactness fails at the level of first uncountable cardinal and to which extent it could be recovered on some other perhaps not so large cardinal. While this is of great interest to set theorists, one of the main motivations behind this line of research is in its applicability to other areas of mathematics. We give some details about this and we expose some possible directions for further (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  • A Dual Open Coloring Axiom.Stefan Geschke - 2006 - Annals of Pure and Applied Logic 140 (1):40-51.
    We discuss a dual of the Open Coloring Axiom introduced by Abraham et al. [U. Abraham, M. Rubin, S. Shelah, On the consistency of some partition theorems for continuous colorings, and the structure of 1-dense real order types, Ann. Pure Appl. Logic 29 123–206] and show that it follows from a statement about continuous colorings on Polish spaces that is known to be consistent. We mention some consequences of the new axiom and show that implies that all cardinal invariants in (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Sacks Forcing, Laver Forcing, and Martin's Axiom.Haim Judah, Arnold W. Miller & Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (3):145-161.
    In this paper we study the question assuming MA+⌝CH does Sacks forcing or Laver forcing collapse cardinals? We show that this question is equivalent to the question of what is the additivity of Marczewski's ideals 0. We give a proof that it is consistent that Sacks forcing collapses cardinals. On the other hand we show that Laver forcing does not collapse cardinals.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  • Chain Conditions of Products, and Weakly Compact Cardinals.Assaf Rinot - 2014 - Bulletin of Symbolic Logic 20 (3):293-314,.
    The history of productivity of the κ-chain condition in partial orders, topological spaces, or Boolean algebras is surveyed, and its connection to the set-theoretic notion of a weakly compact cardinal is highlighted. Then, it is proved that for every regular cardinal κ > א1, the principle □ is equivalent to the existence of a certain strong coloring c : [κ]2 → κ for which the family of fibers T is a nonspecial κ-Aronszajn tree. The theorem follows from an analysis of (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  • Maximal Chains Inωω and Ultrapowers of the Integers.Saharon Shelah & Juris Steprāns - 1993 - Archive for Mathematical Logic 32 (5):305-319.
    Various questions posed by P. Nyikos concerning ultrafilters on ω and chains in the partial order (ω, <*) are answered. The main tool is the oracle chain condition and variations of it.
    No categories
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations