This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related categories

431 found
Order:
1 — 50 / 431
Material to categorize
  1. Tarski Alfred. Axiomatic and Algebraic Aspects of Two Theorems on Sums of Cardinals. Ebd., S. 79–104.W. Ackermann - 1950 - Journal of Symbolic Logic 14 (4):257-258.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  2. Department of Computer Science. Eotvos University, Rakoczi Ut 5, H-1088 Budapest VIII, Hungary, Kope@ Cs. Elte. Hu. Ten Papers by Arthur Apter on Large Cardinals Arthur W. After. On the Least Strongly Compact Cardinal. Israeljournal of Mathematics, Vol. 35 (1980). Pp. 225-233. [REVIEW]S. Aharon Shelah - 2000 - Bulletin of Symbolic Logic 6:86.
  3. Baire Category on Cardinals.C. Alkor & B. Intrigila - 1983 - Mathematical Logic Quarterly 29 (4):245-252.
  4. Games, Scales, and Suslin Cardinals. The Cabal Seminar, Volume I. [REVIEW]Alessandro Andretta - 2012 - Bulletin of Symbolic Logic 18 (1):122-125.
  5. Large Cardinals and Iteration Trees of Height Ω.Alessandro Andretta - 1991 - Annals of Pure and Applied Logic 54 (1):1-15.
    In this paper we continue the line of work initiated in “Building iteration trees”. It is shown that the existence of a certain kind of iteration tree of height ω is equivalent to the existence of a cardinal δ that is Woodin with respect to functions in the next admissible.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  6. Removing Laver Functions From Supercompactness Arguments.A. W. Apter - 2005 - Mathematical Logic Quarterly 51 (2):154.
    We show how the use of a Laver function in the proof of the consistency, relative to the existence of a supercompact cardinal, of both the Proper Forcing Axiom and the Semiproper Forcing Axiom can be eliminated via the use of lottery sums of the appropriate partial orderings.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  7. Level by Level Equivalence and Strong Compactness.A. W. Apter - 2004 - Mathematical Logic Quarterly 50 (1):51.
    We force and construct models in which there are non-supercompact strongly compact cardinals which aren't measurable limits of strongly compact cardinals and in which level by level equivalence between strong compactness and supercompactness holds non-trivially except at strongly compact cardinals. In these models, every measurable cardinal κ which isn't either strongly compact or a witness to a certain phenomenon first discovered by Menas is such that for every regular cardinal λ > κ, κ is λ strongly compact iff κ is (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  8. Failure of GCH and the Level by Level Equivalence Between Strong Compactness and Supercompactness.A. W. Apter - 2003 - Mathematical Logic Quarterly 49 (6):587.
    We force and obtain three models in which level by level equivalence between strong compactness and supercompactness holds and in which, below the least supercompact cardinal, GCH fails unboundedly often. In two of these models, GCH fails on a set having measure 1 with respect to certain canonical measures. There are no restrictions in all of our models on the structure of the class of supercompact cardinals.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  9. Strong Cardinals Can Be Fully Laver Indestructible.A. W. Apter - 2002 - Mathematical Logic Quarterly 48 (4):499-507.
    We prove three theorems which show that it is relatively consistent for any strong cardinal κ to be fully Laver indestructible under κ-directed closed forcing.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  10. Strong Compactness and a Global Version of a Theorem of Ben-David and Magidor.A. W. Apter - 2000 - Mathematical Logic Quarterly 46 (4):453-460.
    Starting with a model in which κ is the least inaccessible limit of cardinals δ which are δ+ strongly compact, we force and construct a model in which κ remains inaccessible and in which, for every cardinal γ < κ, □γ+ω fails but □γ+ω, ω holds. This generalizes a result of Ben-David and Magidor and provides an analogue in the context of strong compactness to a result of the author and Cummings in the context of supercompactness.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  11. Indestructibility and Destructible Measurable Cardinals.Arthur W. Apter - 2016 - Archive for Mathematical Logic 55 (1-2):3-18.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  12. Inaccessible Cardinals, Failures of GCH, and Level-by-Level Equivalence.Arthur W. Apter - 2014 - Notre Dame Journal of Formal Logic 55 (4):431-444.
    We construct models for the level-by-level equivalence between strong compactness and supercompactness containing failures of the Generalized Continuum Hypothesis at inaccessible cardinals. In one of these models, no cardinal is supercompact up to an inaccessible cardinal, and for every inaccessible cardinal $\delta $, $2^{\delta }\gt \delta ^{++}$. In another of these models, no cardinal is supercompact up to an inaccessible cardinal, and the only inaccessible cardinals at which GCH holds are also measurable. These results extend and generalize earlier work of (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  13. Indestructible Strong Compactness and Level by Level Inequivalence.Arthur W. Apter - 2013 - Mathematical Logic Quarterly 59 (4-5):371-377.
  14. Indestructibility, Measurability, and Degrees of Supercompactness.Arthur W. Apter - 2012 - Mathematical Logic Quarterly 58 (1):75-82.
    Suppose that κ is indestructibly supercompact and there is a measurable cardinal λ > κ. It then follows that A1 = {δ < κ∣δ is measurable, δ is not a limit of measurable cardinals, and δ is not δ+ supercompact} is unbounded in κ. If in addition λ is 2λ supercompact, then A2 = {δ < κ∣δ is measurable, δ is not a limit of measurable cardinals, and δ is δ+ supercompact} is unbounded in κ as well. The large cardinal (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  15. On Some Questions Concerning Strong Compactness.Arthur W. Apter - 2012 - Archive for Mathematical Logic 51 (7-8):819-829.
    A question of Woodin asks if κ is strongly compact and GCH holds below κ, then must GCH hold everywhere? One variant of this question asks if κ is strongly compact and GCH fails at every regular cardinal δ < κ, then must GCH fail at some regular cardinal δ ≥ κ? Another variant asks if it is possible for GCH to fail at every limit cardinal less than or equal to a strongly compact cardinal κ. We get a negative (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  16. A Remark on the Tree Property in a Choiceless Context.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (5-6):585-590.
    We show that the consistency of the theory “ZF + DC + Every successor cardinal is regular + Every limit cardinal is singular + Every successor cardinal satisfies the tree property” follows from the consistency of a proper class of supercompact cardinals. This extends earlier results due to the author showing that the consistency of the theory “ ${{\rm ZF} + \neg{\rm AC}_\omega}$ + Every successor cardinal is regular + Every limit cardinal is singular + Every successor cardinal satisfies the (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  17. Indestructibility, HOD, and the Ground Axiom.Arthur W. Apter - 2011 - Mathematical Logic Quarterly 57 (3):261-265.
    Let φ1 stand for the statement V = HOD and φ2 stand for the Ground Axiom. Suppose Ti for i = 1, …, 4 are the theories “ZFC + φ1 + φ2,” “ZFC + ¬φ1 + φ2,” “ZFC + φ1 + ¬φ2,” and “ZFC + ¬φ1 + ¬φ2” respectively. We show that if κ is indestructibly supercompact and λ > κ is inaccessible, then for i = 1, …, 4, Ai = df{δ κ is inaccessible. We show it is also (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  18. Level by Level Inequivalence Beyond Measurability.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (7-8):707-712.
    We construct models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In each model, above the supercompact cardinal, there are finitely many strongly compact cardinals, and the strongly compact and measurable cardinals precisely coincide.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  19. How Many Normal Measures Can ℵ Ω 1+1 Carry?Arthur W. Apter - 2010 - Mathematical Logic Quarterly 56 (2):164-170.
    Relative to the existence of a supercompact cardinal with a measurable cardinal above it, we show that it is consistent for ℵ1 to be regular and for ℵmath image to be measurable and to carry precisely τ normal measures, where τ ≥ ℵmath image is any regular cardinal. This extends the work of [2], in which the analogous result was obtained for ℵω +1 using the same hypotheses.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  20. Indestructibility, Instances of Strong Compactness, and Level by Level Inequivalence.Arthur W. Apter - 2010 - Archive for Mathematical Logic 49 (7-8):725-741.
    Suppose λ > κ is measurable. We show that if κ is either indestructibly supercompact or indestructibly strong, then A = {δ < κ | δ is measurable, yet δ is neither δ + strongly compact nor a limit of measurable cardinals} must be unbounded in κ. The large cardinal hypothesis on λ is necessary, as we further demonstrate by constructing via forcing two models in which ${A = \emptyset}$ . The first of these contains a supercompact cardinal κ and (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  21. Tallness and Level by Level Equivalence and Inequivalence.Arthur W. Apter - 2010 - Mathematical Logic Quarterly 56 (1):4-12.
    We construct two models containing exactly one supercompact cardinal in which all non-supercompact measurable cardinals are strictly taller than they are either strongly compact or supercompact. In the first of these models, level by level equivalence between strong compactness and supercompactness holds. In the other, level by level inequivalence between strong compactness and supercompactness holds. Each universe has only one strongly compact cardinal and contains relatively few large cardinals.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  22. Indestructibility and Stationary Reflection.Arthur W. Apter - 2009 - Mathematical Logic Quarterly 55 (3):228-236.
    If κ < λ are such that κ is a strong cardinal whose strongness is indestructible under κ -strategically closed forcing and λ is weakly compact, then we show thatA = {δ < κ | δ is a non-weakly compact Mahlo cardinal which reflects stationary sets}must be unbounded in κ. This phenomenon, however, need not occur in a universe with relatively few large cardinals. In particular, we show how to construct a model where no cardinal is supercompact up to a (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  23. Indestructibility Under Adding Cohen Subsets and Level by Level Equivalence.Arthur W. Apter - 2009 - Mathematical Logic Quarterly 55 (3):271-279.
    We construct a model for the level by level equivalence between strong compactness and supercompactness in which the least supercompact cardinal κ has its strong compactness indestructible under adding arbitrarily many Cohen subsets. There are no restrictions on the large cardinal structure of our model.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  24. Indestructibility and Measurable Cardinals with Few and Many Measures.Arthur W. Apter - 2008 - Archive for Mathematical Logic 47 (2):101-110.
    If κ < λ are such that κ is indestructibly supercompact and λ is measurable, then we show that both A = {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ carries the maximal number of normal measures} and B = {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ carries fewer than the maximal number of normal measures} are unbounded (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  25. Reducing the Consistency Strength of an Indestructibility Theorem.Arthur W. Apter - 2008 - Mathematical Logic Quarterly 54 (3):288-293.
    Using an idea of Sargsyan, we show how to reduce the consistency strength of the assumptions employed to establish a theorem concerning a uniform level of indestructibility for both strong and supercompact cardinals.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  26. Indestructibility and Level by Level Equivalence and Inequivalence.Arthur W. Apter - 2007 - Mathematical Logic Quarterly 53 (1):78-85.
    If κ < λ are such that κ is indestructibly supercompact and λ is 2λ supercompact, it is known from [4] that {δ < κ | δ is a measurable cardinal which is not a limit of measurable cardinals and δ violates level by level equivalence between strong compactness and supercompactness}must be unbounded in κ. On the other hand, using a variant of the argument used to establish this fact, it is possible to prove that if κ < λ are (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   4 citations  
  27. Supercompactness and Level by Level Equivalence Are Compatible with Indestructibility for Strong Compactness.Arthur W. Apter - 2007 - Archive for Mathematical Logic 46 (3-4):155-163.
    It is known that if $\kappa < \lambda$ are such that κ is indestructibly supercompact and λ is 2λ supercompact, then level by level equivalence between strong compactness and supercompactness fails. We prove a theorem which points towards this result being best possible. Specifically, we show that relative to the existence of a supercompact cardinal, there is a model for level by level equivalence between strong compactness and supercompactness containing a supercompact cardinal κ in which κ’s strong compactness is indestructible (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  28. Failures of SCH and Level by Level Equivalence.Arthur W. Apter - 2006 - Archive for Mathematical Logic 45 (7):831-838.
    We construct a model for the level by level equivalence between strong compactness and supercompactness in which below the least supercompact cardinal κ, there is a stationary set of cardinals on which SCH fails. In this model, the structure of the class of supercompact cardinals can be arbitrary.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  29. Supercompactness and Measurable Limits of Strong Cardinals II: Applications to Level by Level Equivalence.Arthur W. Apter - 2006 - Mathematical Logic Quarterly 52 (5):457-463.
    We construct models for the level by level equivalence between strong compactness and supercompactness in which for κ the least supercompact cardinal and δ ≤ κ any cardinal which is either a strong cardinal or a measurable limit of strong cardinals, 2δ > δ+ and δ is < 2δ supercompact. In these models, the structure of the class of supercompact cardinals can be arbitrary, and the size of the power set of κ can essentially be made as large as desired. (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  30. The Least Strongly Compact Can Be the Least Strong and Indestructible.Arthur W. Apter - 2006 - Annals of Pure and Applied Logic 144 (1):33-42.
    We construct two models in which the least strongly compact cardinal κ is also the least strong cardinal. In each of these models, κ satisfies indestructibility properties for both its strong compactness and strongness.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  31. Universal Partial Indestructibility and Strong Compactness.Arthur W. Apter - 2005 - Mathematical Logic Quarterly 51 (5):524-531.
    For any ordinal δ, let λδ be the least inaccessible cardinal above δ. We force and construct a model in which the least supercompact cardinal κ is indestructible under κ-directed closed forcing and in which every measurable cardinal δ < κ is < λδ strongly compact and has its < λδ strong compactness indestructible under δ-directed closed forcing of rank less than λδ. In this model, κ is also the least strongly compact cardinal. We also establish versions of this result (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  32. Diamond, Square, and Level by Level Equivalence.Arthur W. Apter - 2004 - Archive for Mathematical Logic 44 (3):387-395.
    We force and construct a model in which level by level equivalence between strong compactness and supercompactness holds, along with certain additional combinatorial properties. In particular, in this model, ♦ δ holds for every regular uncountable cardinal δ, and below the least supercompact cardinal κ, □ δ holds on a stationary subset of κ. There are no restrictions in our model on the structure of the class of supercompact cardinals.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  33. On a Problem of Foreman and Magidor.Arthur W. Apter - 2004 - Archive for Mathematical Logic 44 (4):493-498.
    A question of Foreman and Magidor asks if it is consistent for every sequence of stationary subsets of the ℵ n ’s for 1≤n<ω to be mutually stationary. We get a positive answer to this question in the context of the negation of the Axiom of Choice. We also indicate how a positive answer to a generalized version of this question in a choiceless context may be obtained.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  34. Characterizing Strong Compactness Via Strongness.Arthur W. Apter - 2003 - Mathematical Logic Quarterly 49 (4):375.
    We construct a model in which the strongly compact cardinals can be non-trivially characterized via the statement “κ is strongly compact iff κ is a measurable limit of strong cardinals”. If our ground model contains large enough cardinals, there will be supercompact cardinals in the universe containing this characterization of the strongly compact cardinals.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  35. Some Remarks on Indestructibility and Hamkins' Lottery Preparation.Arthur W. Apter - 2003 - Archive for Mathematical Logic 42 (8):717-735.
  36. Forcing the Least Measurable to Violate GCH.Arthur W. Apter - 1999 - Mathematical Logic Quarterly 45 (4):551-560.
    Starting with a model for “GCH + k is k+ supercompact”, we force and construct a model for “k is the least measurable cardinal + 2k = K+”. This model has the property that forcing over it with Add preserves the fact k is the least measurable cardinal.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  37. More on the Least Strongly Compact Cardinal.Arthur W. Apter - 1997 - Mathematical Logic Quarterly 43 (3):427-430.
    We show that it is consistent, relative to a supercompact limit of supercompact cardinals, for the least strongly compact cardinal k to be both the least measurable cardinal and to be > 2k supercompact.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  38. Patterns of Compact Cardinals.Arthur W. Apter - 1997 - Annals of Pure and Applied Logic 89 (2-3):101-115.
    We show relative to strong hypotheses that patterns of compact cardinals in the universe, where a compact cardinal is one which is either strongly compact or supercompact, can be virtually arbitrary. Specifically, we prove if V “ZFC + Ω is the least inaccessible limit of measurable limits of supercompact cardinals + ƒ : Ω → 2 is a function”, then there is a partial ordering P V so that for , There is a proper class of compact cardinals + If (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   11 citations  
  39. A Cardinal Pattern Inspired by AD.Arthur W. Apter - 1996 - Mathematical Logic Quarterly 42 (1):211-218.
    Assuming Con, a model in which there are unboundedly many regular cardinals below Θ and in which the only regular cardinals below Θ are limit cardinals was previously constructed. Using a large cardinal hypothesis far beyond Con, we construct in this paper a model in which there is a proper class of regular cardinals and in which the only regular cardinals in the universe are limit cardinals.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  40. Some New Upper Bounds in Consistency Strength for Certain Choiceless Large Cardinal Patterns.Arthur W. Apter - 1992 - Archive for Mathematical Logic 31 (3):201-205.
    In this paper, we show that certain choiceless models of ZF originally constructed using an almost huge cardinal can be constructed using cardinals strictly weaker in consistency strength.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  41. Some Results on Consecutive Large Cardinals.Arthur W. Apter - 1983 - Annals of Pure and Applied Logic 25 (1):1-17.
    We obtain 2 models in which AC is false and in which there are long sequences of consecutive large cardinals.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    My bibliography   6 citations  
  42. An L-Like Model Containing Very Large Cardinals.Arthur W. Apter & James Cummings - 2008 - Archive for Mathematical Logic 47 (1):65-78.
    We force and construct a model in which level by level equivalence between strong compactness and supercompactness holds, along with a strong form of diamond and a version of square consistent with supercompactness. This generalises a result due to the first author. There are no restrictions in our model on the structure of the class of supercompact cardinals.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  43. Coding Into HOD Via Normal Measures with Some Applications.Arthur W. Apter & Shoshana Friedman - 2011 - Mathematical Logic Quarterly 57 (4):366-372.
    We develop a new method for coding sets while preserving GCH in the presence of large cardinals, particularly supercompact cardinals. We will use the number of normal measures carried by a measurable cardinal as an oracle, and therefore, in order to code a subset A of κ, we require that our model contain κ many measurable cardinals above κ. Additionally we will describe some of the applications of this result. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  44. Indestructible Strong Compactness but Not Supercompactness.Arthur W. Apter, Moti Gitik & Grigor Sargsyan - 2012 - Annals of Pure and Applied Logic 163 (9):1237-1242.
  45. Inner Models with Large Cardinal Features Usually Obtained by Forcing.Arthur W. Apter, Victoria Gitman & Joel David Hamkins - 2012 - Archive for Mathematical Logic 51 (3-4):257-283.
    We construct a variety of inner models exhibiting features usually obtained by forcing over universes with large cardinals. For example, if there is a supercompact cardinal, then there is an inner model with a Laver indestructible supercompact cardinal. If there is a supercompact cardinal, then there is an inner model with a supercompact cardinal κ for which 2 κ = κ +, another for which 2 κ = κ ++ and another in which the least strongly compact cardinal is supercompact. (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  46. Large Cardinal Structures Below $Aleph_omega$.Arthur W. Apter & James M. Henle - 1986 - Journal of Symbolic Logic 51 (3):591-603.
  47. Making All Cardinals Almost Ramsey.Arthur W. Apter & Peter Koepke - 2008 - Archive for Mathematical Logic 47 (7-8):769-783.
    We examine combinatorial aspects and consistency strength properties of almost Ramsey cardinals. Without the Axiom of Choice, successor cardinals may be almost Ramsey. From fairly mild supercompactness assumptions, we construct a model of ZF + ${\neg {\rm AC}_\omega}$ in which every infinite cardinal is almost Ramsey. Core model arguments show that strong assumptions are necessary. Without successors of singular cardinals, we can weaken this to an equiconsistency of the following theories: “ZFC + There is a proper class of regular almost (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  48. An Equiconsistency for Universal Indestructibility.Arthur W. Apter & Grigor Sargsyan - 2010 - Journal of Symbolic Logic 75 (1):314-322.
    We obtain an equiconsistency for a weak form of universal indestructibility for strongness. The equiconsistency is relative to a cardinal weaker in consistency strength than a Woodin cardinal. Stewart Baldwin's notion of hyperstrong cardinal. We also briefly indicate how our methods are applicable to universal indestructibility for supercompactness and strong compactness.
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  49. Universal Indestructibility for Degrees of Supercompactness and Strongly Compact Cardinals.Arthur W. Apter & Grigor Sargsyan - 2008 - Archive for Mathematical Logic 47 (2):133-142.
    We establish two theorems concerning strongly compact cardinals and universal indestructibility for degrees of supercompactness. In the first theorem, we show that universal indestructibility for degrees of supercompactness in the presence of a strongly compact cardinal is consistent with the existence of a proper class of measurable cardinals. In the second theorem, we show that universal indestructibility for degrees of supercompactness is consistent in the presence of two non-supercompact strongly compact cardinals, each of which exhibits a significant amount of indestructibility (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  50. Identity Crises and Strong Compactness III: Woodin Cardinals. [REVIEW]Arthur W. Apter & Grigor Sargsyan - 2005 - Archive for Mathematical Logic 45 (3):307-322.
    We show that it is consistent, relative to n ∈ ω supercompact cardinals, for the strongly compact and measurable Woodin cardinals to coincide precisely. In particular, it is consistent for the first n strongly compact cardinals to be the first n measurable Woodin cardinals, with no cardinal above the n th strongly compact cardinal being measurable. In addition, we show that it is consistent, relative to a proper class of supercompact cardinals, for the strongly compact cardinals and the cardinals which (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
1 — 50 / 431