Results for 'S. Shelah'

(not author) ( search as author name )
1000+ found
Order:
  1. Martin's Axioms, Measurability and Equiconsistency Results.Jaime I. Ihoda & Saharon Shelah - 1989 - Journal of Symbolic Logic 54 (1):78-94.
    We deal with the consistency strength of ZFC + variants of MA + suitable sets of reals are measurable (and/or Baire, and/or Ramsey). We improve the theorem of Harrington and Shelah [2] repairing the asymmetry between measure and category, obtaining also the same result for Ramsey. We then prove parallel theorems with weaker versions of Martin's axiom (MA(σ-centered), (MA(σ-linked)), MA(Γ + ℵ 0 ), MA(K)), getting Mahlo, inaccessible and weakly compact cardinals respectively. We prove that if there exists r (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  2.  8
    Borel Partitions of Infinite Subtrees of a Perfect Tree.A. Louveau, S. Shelah & B. Veličković - 1993 - Annals of Pure and Applied Logic 63 (3):271-281.
    Louveau, A., S. Shelah and B. Velikovi, Borel partitions of infinite subtrees of a perfect tree, Annals of Pure and Applied Logic 63 271–281. We define a notion of type of a perfect tree and show that, for any given type τ, if the set of all subtrees of a given perfect tree T which have type τ is partitioned into two Borel classes then there is a perfect subtree S of T such that all subtrees of S of (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  3.  5
    Kaplansky's Problem on Valuation RingsA Transfer Theorem for Nonstandard UniserialsOn a Conjecture Regarding Nonstandard Uniserial ModulesExplicitly Non-Standard Uniserial Modules.Birge Huisgen-Zimmermann, Laszlo Fuchs, Saharon Shelah, Paul C. Eklof, P. C. Eklof & S. Shelah - 2002 - Bulletin of Symbolic Logic 8 (3):441.
  4. Baldwin, JT and Holland, K., Constructing Ω-Stable Struc-Tures: Model Completeness (1–3) 159–172 Berarducci, A. And Servi, T., An Effective Version of Wilkie's Theorem of the Complement and Some Effective o-Minimality Results (1–3) 43–74. [REVIEW]R. Downey, A. Li, G. Wu, M. Dzˇamonja & S. Shelah - 2004 - Annals of Pure and Applied Logic 125:173.
  5.  6
    On Distinguishing Quotients of Symmetric Groups.S. Shelah & J. K. Truss - 1999 - Annals of Pure and Applied Logic 97 (1-3):47-83.
    A study of the elementary theory of quotients of symmetric groups is carried out in a similar spirit to Shelah . Apart from the trivial and alternating subgroups, the normal subgroups of the full symmetric group S on an infinite cardinal μ are all of the form Sκ = the subgroup consisting of elements whose support has cardinality 20, cƒ 20 < κ, 0 < κ < 20, and κ = 0, we make a further analysis of the first (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark  
  6.  16
    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   13 citations  
  7.  6
    Creature Forcing and Five Cardinal Characteristics in Cichoń’s Diagram.Arthur Fischer, Martin Goldstern, Jakob Kellner & Saharon Shelah - 2017 - Archive for Mathematical Logic 56 (7-8):1045-1103.
    We use a creature construction to show that consistently $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$The same method shows the consistency of $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$.
    No categories
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  8.  10
    More on SOP 1 and SOP 2.Saharon Shelah & Alexander Usvyatsov - 2008 - Annals of Pure and Applied Logic 155 (1):16-31.
    This paper continues the work in [S. Shelah, Towards classifying unstable theories, Annals of Pure and Applied Logic 80 229–255] and [M. Džamonja, S. Shelah, On left triangle, open*-maximality, Annals of Pure and Applied Logic 125 119–158]. We present a rank function for NSOP1 theories and give an example of a theory which is NSOP1 but not simple. We also investigate the connection between maximality in the ordering left triangle, open* among complete first order theories and the SOP2 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  9.  6
    Combinatorial Properties of Hechler Forcing.Jörg Brendle, Haim Judah & Saharon Shelah - 1992 - Annals of Pure and Applied Logic 58 (3):185-199.
    Brendle, J., H. Judah and S. Shelah, Combinatorial properties of Hechler forcing, Annals of Pure and Applied Logic 59 185–199. Using a notion of rank for Hechler forcing we show: assuming ωV1 = ωL1, there is no real in V[d] which is eventually different from the reals in L[ d], where d is Hechler over V; adding one Hechler real makes the invariants on the left-hand side of Cichoń's diagram equal ω1 and those on the right-hand side equal 2ω (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  10.  8
    The Universality Spectrum of Stable Unsuperstable Theories.Menachem Kojman & Saharon Shelah - 1992 - Annals of Pure and Applied Logic 58 (1):57-72.
    Kojman, M. and S. Shelah, The universality spectrum of stable unsuperstable theories, Annals of Pure and Applied Logic 58 57–72. It is shown that if T is stable unsuperstable, and 1 [brvbar]T[brvbar], T stable and κ<κ then there is a universal tree of height κ + 1 in cardinality λ.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  11. The Lazy Model-Theoretician's Guide to Stability.Saharon Shelah - 1975 - Logique Et Analyse 18 (71):72.
    No categories
     
    Export citation  
     
    Bookmark   8 citations  
  12.  44
    Superdestructibility: A Dual to Laver's Indestructibility.Joel David Hamkins & Saharon Shelah - 1998 - Journal of Symbolic Logic 63 (2):549-554.
    After small forcing, any $ -closed forcing will destroy the supercompactness and even the strong compactness of κ.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  13.  13
    Closed Measure Zero Sets.Tomek Bartoszynski & Saharon Shelah - 1992 - Annals of Pure and Applied Logic 58 (2):93-110.
    Bartoszynski, T. and S. Shelah, Closed measure zero sets, Annals of Pure and Applied Logic 58 93–110. We study the relationship between the σ-ideal generated by closed measure zero sets and the ideals of null and meager sets. We show that the additivity of the ideal of closed measure zero sets is not bigger than covering for category. As a consequence we get that the additivity of the ideal of closed measure zero sets is equal to the additivity of (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  14.  35
    Martin's Axiom and Well-Ordering of the Reals.Uri Abraham & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5):287-298.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  15.  23
    Martin's Axiom and $\Delta^2_1$ Well-Ordering of the Reals.Uri Abraham & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5-6):287-298.
    Assuming an inaccessible cardinal $\kappa$ , there is a generic extension in which $MA + 2^{\aleph_0} = \kappa$ holds and the reals have a $\Delta^2_1$ well-ordering.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  16.  2
    Κ -Bounded Exponential-Logarithmic Power Series Fields.Salma Kuhlmann & Saharon Shelah - 2005 - Annals of Pure and Applied Logic 136 (3):284-296.
    In [F.-V. Kuhlmann, S. Kuhlmann, S. Shelah, Exponentiation in power series fields, Proc. Amer. Math. Soc. 125 3177–3183] it was shown that fields of generalized power series cannot admit an exponential function. In this paper, we construct fields of generalized power series with bounded support which admit an exponential. We give a natural definition of an exponential, which makes these fields into models of real exponentiation. The method allows us to construct for every κ regular uncountable cardinal, 2κ pairwise (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  17.  4
    Rabin's Uniformization Problem.Yuri Gurevich & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (4):1105-1119.
    The set of all words in the alphabet {l, r} forms the full binary tree T. If x ∈ T then xl and xr are the left and the right successors of x respectively. We consider the monadic second-order language of the full binary tree with the two successor relations. This language allows quantification over elements of T and over arbitrary subsets of T. We prove that there is no monadic second-order formula φ * (X, y) such that for every (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  18.  2
    On Fleissner's Diamond.Saharon Shelah - 1981 - Notre Dame Journal of Formal Logic 22 (1):29-35.
  19.  14
    On ◁∗-Maximality.Mirna Džamonja & Saharon Shelah - 2004 - Annals of Pure and Applied Logic 125 (1-3):119-158.
    This paper investigates a connection between the semantic notion provided by the ordering * among theories in model theory and the syntactic SOPn hierarchy of Shelah. It introduces two properties which are natural extensions of this hierarchy, called SOP2 and SOP1. It is shown here that SOP3 implies SOP2 implies SOP1. In Shelah's article 229) it was shown that SOP3 implies *-maximality and we prove here that *-maximality in a model of GCH implies a property called SOP2″. It (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   14 citations  
  20.  4
    Calude, C., Calude, E. And Khoussainov, B., Deterministic.S. Fuchino, S. Shelah, L. Soukup, M. Gitik, C. Merimovich, R. Laver, S. Riis, P. Sewell, S. Soloviev & O. Spinas - 1997 - Annals of Pure and Applied Logic 90 (1-3):277.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  21.  8
    Models with Second Order Properties IV. A General Method and Eliminating Diamonds.Saharon Shelah - 1983 - Annals of Pure and Applied Logic 25 (2):183-212.
    We show how to build various models of first-order theories, which also have properties like: tree with only definable branches, atomic Boolean algebras or ordered fields with only definable automorphisms. For this we use a set-theoretic assertion, which may be interesting by itself on the existence of quite generic subsets of suitable partial orders of power λ + , which follows from ♦ λ and even weaker hypotheses . For a related assertion, which is equivalent to the morass see (...) and Stanley [16]. The various specific constructions serve also as examples of how to use this set-theoretic lemma. We apply the method to construct rigid ordered fields, rigid atomic Boolean algebras, trees with only definable branches; all in successors of regular cardinals under appropriate set- theoretic assumptions. So we are able to answer the following algebraic question. Saltzman's Question . Is there a rigid real closed field, which is not a subfield of the reals? (shrink)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  22.  7
    More on Simple Forcing Notions and Forcings with Ideals.M. Gitik & S. Shelah - 1993 - Annals of Pure and Applied Logic 59 (3):219-238.
    It is shown that cardinals below a real-valued measurable cardinal can be split into finitely many intervals so that the powers of cardinals from the same interval are the same. This generalizes a theorem of Prikry [9]. Suppose that the forcing with a κ-complete ideal over κ is isomorphic to the forcing of λ-Cohen or random reals. Then for some τ<κ, λτ2κ and λ2<κ implies that 2κ=2τ= cov. In particular, if 2κ<κ+ω, then λ=2κ. This answers a question from [3]. If (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  23.  12
    Models with Second Order Properties V: A General Principle.Saharon Shelah, Claude Laflamme & Bradd Hart - 1993 - Annals of Pure and Applied Logic 64 (2):169-194.
    Shelah, S., C. Laflamme and B. Hart, Models with second order properties V: A general principle, Annals of Pure and Applied Logic 64 169–194. We present a general framework for carrying out the construction in [2-10] and others of the same type. The unifying factor is a combinatorial principle which we present in terms of a game in which the first player challenges the second player to carry out constructions which would be much easier in a generic extension of (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  24.  14
    On Ultraproducts of Boolean Algebras and Irr.Saharon Shelah - 2003 - Archive for Mathematical Logic 42 (6):569-581.
    1. Consistent inequality [We prove the consistency of irr $(\displaystyle\prod_{i < \kappa} B_i/D) < \displaystyle\prod_{i < \kappa}$ irr(B i )/D where D is an ultrafilter on κ and each B i is a Boolean algebra and irr(B) is the maximal size of irredundant subsets of a Boolean algebra B, see full definition in the text. This solves the last problem, 35, of this form from Monk's list of problems in [M2]. The solution applies to many other properties, e.g. Souslinity.] 2. (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  25. Fellows, MR, See Cesati, M.M. Gitik, W. J. Mitchell, T. Glafi, T. Strahm, M. Grohe, G. Hjorth, A. S. Kechris, S. Shelah & X. Yi - 1996 - Annals of Pure and Applied Logic 82:343.
     
    Export citation  
     
    Bookmark  
  26.  19
    On Some Configurations Related to the Shelah Weak Hypothesis.Moti Gitik & Saharon Shelah - 2001 - Archive for Mathematical Logic 40 (8):639-650.
    We show that some cardinal arithmetic configurations related to the negation of the Shelah Weak Hypothesis and natural from the forcing point of view are impossible.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  27.  20
    Second-Order Quantifiers and the Complexity of Theories.J. T. Baldwin & S. Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (3):229-303.
  28. On the Structure of $\Operatorname{Ext}(a, \Mathbf{Z})$ in ZFC+.G. Sageev & S. Shelah - 1985 - Journal of Symbolic Logic 50 (2):302 - 315.
  29.  7
    Positive Results in Abstract Model Theory: A Theory of Compact Logics.J. A. Makowsky & S. Shelah - 1983 - Annals of Pure and Applied Logic 25 (3):263-299.
    We prove that compactness is equivalent to the amalgamation property, provided the occurrence number of the logic is smaller than the first uncountable measurable cardinal. We also relate compactness to the existence of certain regular ultrafilters related to the logic and develop a general theory of compactness and its consequences. We also prove some combinatorial results of independent interest.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  30.  8
    The Primal Framework II: Smoothness.J. T. Baldwin & S. Shelah - 1991 - Annals of Pure and Applied Logic 55 (1):1-34.
    Let be a class of models with a notion of ‘strong’ submodel and of canonically prime model over an increasing chain. We show under appropriate set-theoretic hypotheses that if K is not smooth , then K has many models in certain cardinalities. On the other hand, if K is smooth, we show that in reasonable cardinalities K has a unique homogeneous-universal model. In this situation we introduce the notion of type and prove the equivalence of saturated with homogeneous-universal.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  31.  4
    The Primal Framework I.J. T. Baldwin & S. Shelah - 1990 - Annals of Pure and Applied Logic 46 (3):235-264.
  32.  17
    On the Existence of Atomic Models.M. C. Laskowski & S. Shelah - 1993 - Journal of Symbolic Logic 58 (4):1189-1194.
    We give an example of a countable theory $T$ such that for every cardinal $\lambda \geq \aleph_2$ there is a fully indiscernible set $A$ of power $\lambda$ such that the principal types are dense over $A$, yet there is no atomic model of $T$ over $A$. In particular, $T$ is a theory of size $\lambda$ where the principal types are dense, yet $T$ has no atomic model.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  33.  18
    Isomorphic but Not Lower Base-Isomorphic Cylindric Set Algebras.B. Biró & S. Shelah - 1988 - Journal of Symbolic Logic 53 (3):846-853.
    This paper belongs to cylindric-algebraic model theory understood in the sense of algebraic logic. We show the existence of isomorphic but not lower base-isomorphic cylindric set algebras. These algebras are regular and locally finite. This solves a problem raised in [N 83] which was implicitly present also in [HMTAN 81]. This result implies that a theorem of Vaught for prime models of countable languages does not continue to hold for languages of any greater power.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  34.  10
    Abstract Classes with Few Models Have `Homogeneous-Universal' Models.J. Baldwin & S. Shelah - 1995 - Journal of Symbolic Logic 60 (1):246-265.
  35. Bezem, M., see Barendsen, E.G. M. Bierman, M. DZamonja, S. Shelah, S. Feferman, G. Jiiger, M. A. Jahn, S. Lempp, Sui Yuefei, S. D. Leonhardi & D. Macpherson - 1996 - Annals of Pure and Applied Logic 79 (1):317.
    Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark   3 citations  
  36.  3
    Karp Complexity and Classes with the Independence Property.M. C. Laskowski & S. Shelah - 2003 - Annals of Pure and Applied Logic 120 (1-3):263-283.
    A class K of structures is controlled if for all cardinals λ, the relation of L∞,λ-equivalence partitions K into a set of equivalence classes . We prove that no pseudo-elementary class with the independence property is controlled. By contrast, there is a pseudo-elementary class with the strict order property that is controlled 69–88).
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  37.  2
    Ramsey Ultrafilters and the Reaping Number—Con.M. Goldstern & S. Shelah - 1990 - Annals of Pure and Applied Logic 49 (2):121-142.
    We show that it is consistent that the reaping number r is less than u , the size of the smallest base for an ultrafilter. To show that our forcing preserves certain ultrafilters, we prove a general partition theorem involving Ramsey ideals.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  38.  20
    The Karp Complexity of Unstable Classes.M. C. Laskowski & S. Shelah - 2001 - Archive for Mathematical Logic 40 (2):69-88.
    A class K of structures is controlled if, for all cardinals λ, the relation of L ∞,λ-equivalence partitions K into a set of equivalence classes (as opposed to a proper class). We prove that the class of doubly transitive linear orders is controlled, while any pseudo-elementary class with the ω-independence property is not controlled.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  39. A Graph Which Embeds All Small Graphs on Any Large Set of Vertices.S. Shelah - 1988 - Annals of Pure and Applied Logic 38 (2):171-183.
  40.  24
    Identities on Cardinals Less Than ℵω.M. Gilchrist & S. Shelah - 1996 - Journal of Symbolic Logic 61 (3):780 - 787.
  41.  10
    Remark to “Local Definability Theory” of Reyes.S. Shelah - 1971 - Annals of Mathematical Logic 2 (4):441-447.
  42.  8
    Weakly Compact Cardinals: A Combinatorial Proof.S. Shelah - 1979 - Journal of Symbolic Logic 44 (4):559-562.
  43. Downey, R., F, iiForte, G. And Nies, A., Addendum To.R. Jin, I. Kalantari, L. Welch, B. Khoussainov, R. A. Shore, A. P. Pynko, P. Scowcroft, S. Shelah, J. Zapletal & J. B. Wells - 1999 - Annals of Pure and Applied Logic 98:299.
    No categories
     
    Export citation  
     
    Bookmark   1 citation  
  44.  11
    Forcing Isomorphism.J. T. Baldwin, M. C. Laskowski & S. Shelah - 1993 - Journal of Symbolic Logic 58 (4):1291-1301.
  45.  27
    Forcing Isomorphism II.M. C. Laskowski & S. Shelah - 1996 - Journal of Symbolic Logic 61 (4):1305-1320.
    If T has only countably many complete types, yet has a type of infinite multiplicity then there is a c.c.c. forcing notion Q such that, in any Q-generic extension of the universe, there are non-isomorphic models M 1 and M 2 of T that can be forced isomorphic by a c.c.c. forcing. We give examples showing that the hypothesis on the number of complete types is necessary and what happens if `c.c.c.' is replaced by other cardinal-preserving adjectives. We also give (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  46.  7
    Pointwise Compact and Stable Sets of Measurable Functions.S. Shelah & D. H. Fremlin - 1993 - Journal of Symbolic Logic 58 (2):435-455.
  47. GlaR, T., Rathjen, M. And Schliiter, A., On the Proof-Theoretic.G. Japaridze, R. Jin, S. Shelah, M. Otto, E. Palmgren & M. C. Stanley - 1997 - Annals of Pure and Applied Logic 85:283.
  48.  35
    On the Intersection of Closed Unbounded Sets.U. Abraham & S. Shelah - 1986 - Journal of Symbolic Logic 51 (1):180-189.
    Forcing extensions yield models of ZFC in which a long sequence of club subsets of ω 1 has the following property: every subsequence of size ℵ 1 has a finite intersection.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  49.  9
    Ge Sacks and Sg Simpson [1972] the Oz-Finite Injury Method, Ann. Math. Logic, 4, Pp. 323-367.M. Magidor, S. Shelah, J. Stavi, M. Mytilinaios, Ta Slaman, Jb Paris & H. la KirbyRogers Jr - 1999 - In Edward R. Griffor (ed.), Handbook of Computability Theory. Elsevier. pp. 299.
    Direct download  
     
    Export citation  
     
    Bookmark  
  50.  9
    Identities on Cardinals Less Than $Aleph_omega$.M. Gilchrist & S. Shelah - 1996 - Journal of Symbolic Logic 61 (3):780-787.
1 — 50 / 1000