This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related categories
Subcategories:
111 found
Search inside:
(import / add options)   Sort by:
1 — 50 / 111
Material to categorize
  1. Frederick Bagemihl (1959). Some Results Connected with the Continuum Hypothesis. Mathematical Logic Quarterly 5 (7‐13):97-116.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  2. Everett L. Bull (1978). Successive Large Cardinals. Annals of Mathematical Logic 15 (2):161-191.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  3. Paul Corazza (2010). The Axiom of Infinity and Transformations J: V→V. Bulletin of Symbolic Logic 16 (1):37-84.
    We suggest a new approach for addressing the problem of establishing an axiomatic foundation for large cardinals. An axiom asserting the existence of a large cardinal can naturally be viewed as a strong Axiom of Infinity. However, it has not been clear on the basis of our knowledge of ω itself, or of generally agreed upon intuitions about the true nature of the mathematical universe, what the right strengthening of the Axiom of Infinity is—which large cardinals ought to be derivable? (...)
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  4. Keith J. Devlin (1980). Concerning the Consistency of the Souslin Hypothesis with the Continuum Hypothesis. Annals of Mathematical Logic 19 (1-2):115-125.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  5. F. R. Drake (1973). Review: L. Rieger, On the Consistency of the Generalized Continuum Hypothesis. [REVIEW] Journal of Symbolic Logic 38 (1):153-153.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  6. Sy D. Friedman (2005). Definability Degrees. Mathematical Logic Quarterly 51 (5):448-449.
    We establish the equiconsistency of a simple statement in definability theory with the failure of the GCH at all infinite cardinals. The latter was shown by Foreman and Woodin to be consistent, relative to the existence of large cardinals.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  7. Sy D. Friedman (2005). Genericity and Large Cardinals. Journal of Mathematical Logic 5 (02):149-166.
  8. Sy D. Friedman (2003). Cardinal-Preserving Extensions. Journal of Symbolic Logic 68 (4):1163-1170.
    A classic result of Baumgartner-Harrington-Kleinberg [1] implies that assuming CH a stationary subset of ω1 has a CUB subset in a cardinal-perserving generic extension of V, via a forcing of cardinality ω1. Therefore, assuming that $\omega_2^L$ is countable: { $X \in L \mid X \subseteq \omega_1^L$ and X has a CUB subset in a cardinal -preserving extension of L} is constructible, as it equals the set of constructible subsets of $\omega_1^L$ which in L are stationary. Is there a similar such (...)
    Remove from this list | Direct download (9 more)  
     
    My bibliography  
     
    Export citation  
  9. W. Gielen, H. De Swart & W. Veldman (1981). The Continuum Hypothesis in Intuitionism. Journal of Symbolic Logic 46 (1):121 - 136.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  10. P. K. H. (1967). Set Theory and the Continuum Hypothesis. [REVIEW] Review of Metaphysics 20 (4):716-716.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  11. Stephen H. Hechler (1973). Powers of Singular Cardinals and a Strong Form of The Negation of The Generalized Continuum Hypothesis. Mathematical Logic Quarterly 19 (3‐6):83-84.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  12. Michał Heller & W. H. Woodin (eds.) (2011). Infinity: New Research Frontiers. Cambridge University Press.
    Machine generated contents note: Introduction Rudy Rucker; Part I. Perspectives on Infinity from History: 1. Infinity as a transformative concept in science and theology Wolfgang Achtner; Part II. Perspectives on Infinity from Mathematics: 2. The mathematical infinity Enrico Bombieri; 3. Warning signs of a possible collapse of contemporary mathematics Edward Nelson; Part III. Technical Perspectives on Infinity from Advanced Mathematics: 4. The realm of the infinite W. Hugh Woodin; 5. A potential subtlety concerning the distinction between determinism and nondeterminism W. (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  13. Ignasi Jané (2010). Idealist and Realist Elements in Cantor's Approach to Set Theory. Philosophia Mathematica 18 (2):193-226.
    There is an apparent tension between the open-ended aspect of the ordinal sequence and the assumption that the set-theoretical universe is fully determinate. This tension is already present in Cantor, who stressed the incompletable character of the transfinite number sequence in Grundlagen and avowed the definiteness of the totality of sets and numbers in subsequent philosophical publications and in correspondence. The tension is particularly discernible in his late distinction between sets and inconsistent multiplicities. I discuss Cantor’s contrasting views, and I (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  14. I. Jane (2010). Idealist and Realist Elements in Cantor's Approach to Set Theory. Philosophia Mathematica 18 (2):193-226.
    There is an apparent tension between the open-ended aspect of the ordinal sequence and the assumption that the set-theoretical universe is fully determinate. This tension is already present in Cantor, who stressed the incompletable character of the transfinite number sequence in Grundlagen and avowed the definiteness of the totality of sets and numbers in subsequent philosophical publications and in correspondence. The tension is particularly discernible in his late distinction between sets and inconsistent multiplicities. I discuss Cantor’s contrasting views, and I (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  15. Akihiro Kanamori (1994). The Higher Infinite Large Cardinals in Set Theory From Their Beginnings.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  16. Azriel Levy (1978). Review: Frank R. Drake, Set Theory. An Introduction to Large Cardinals. [REVIEW] Journal of Symbolic Logic 43 (2):384-384.
  17. R. Lubarsky (2008). R. Taschner, The Continuum. Bulletin of Symbolic Logic 14 (2).
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  18. Matthew W. Parker (2013). Set Size and the Part-Whole Principle. Review of Symbolic Logic (4):1-24.
    Recent work has defended “Euclidean” theories of set size, in which Cantor’s Principle (two sets have equally many elements if and only if there is a one-to-one correspondence between them) is abandoned in favor of the Part-Whole Principle (if A is a proper subset of B then A is smaller than B). It has also been suggested that Gödel’s argument for the unique correctness of Cantor’s Principle is inadequate. Here we see from simple examples, not that Euclidean theories of set (...)
    Remove from this list | Direct download (9 more)  
     
    My bibliography  
     
    Export citation  
  19. Esther Ramharter (2009). Christine Redecker. Wittgensteins Philosophie der Mathematik: Eine Neubewertung Im Ausgang Von der Kritik an Cantors Beweis der Überabzählbarkeit der Reellen Zahlen. [Wittgenstein's Philosophy of Mathematics: A Reassessment Starting From the Critique of Cantor's Proof of the Uncountability of the Real Numbers]. Philosophia Mathematica 17 (3):382-392.
    (No abstract is available for this citation).
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  20. Rudolf Taschner & Robert Lubarsky (2008). The Continuum. Bulletin of Symbolic Logic 14 (2):260-261.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  21. José P. Úbeda (1975). Frank R. Drake," Set Theory: An Introduction to Large Cardinals". Teorema: International Journal of Philosophy 5 (3):521-525.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  22. Gabriel Uzquiano (2005). Review of M. Potter, Set Theory and its Philosophy: A Critical Introduction. [REVIEW] Philosophia Mathematica 13 (3):308-346.
The Continuum Hypothesis
  1. Uri Abraham (1983). On Forcing Without the Continuum Hypothesis. Journal of Symbolic Logic 48 (3):658-661.
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  2. C. Alvarez Jimenez (1995). Some Logical Remarks Concerning the Continuum Problem. Boston Studies in the Philosophy of Science 172:173-186.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  3. Arthur W. Apter (2002). Review of J. Cummings, A Model in Which GCH Holds at Successors but Fails at Limits; Strong Ultrapowers and Long Core Models; Coherent Sequences Versus Radin Sequences; and J. Cummings, M. Foreman, and M. Magidor, Squares, Scales and Stationary Reflection. [REVIEW] Bulletin of Symbolic Logic 8 (4):550-552.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  4. Edward G. Belaga (forthcoming). Retrieving the Mathematical Mission of the Continuum Concept From the Transfinitely Reductionist Debris of Cantor’s Paradise. Extended Abstract. International Journal of Pure and Applied Mathematics.
    What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? -/- The double-edged purpose of the present study is to save from the transfinite deadlock of (...)
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  5. John L. Bell (2011). Set Theory: Boolean-Valued Models and Independence Proofs. OUP Oxford.
    This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice.
    Remove from this list |
     
    My bibliography  
     
    Export citation  
  6. David J. Chalmers, Is the Continuum Hypothesis True, False, or Neither?
    Thanks to all the people who responded to my enquiry about the status of the Continuum Hypothesis. This is a really fascinating subject, which I could waste far too much time on. The following is a summary of some aspects of the feeling I got for the problems. This will be old hat to set theorists, and no doubt there are a couple of embarrassing misunderstandings, but it might be of some interest to non professionals.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  7. Justin Clarke-Doane (2013). What is Absolute Undecidability?†. Noûs 47 (3):467-481.
    It is often alleged that, unlike typical axioms of mathematics, the Continuum Hypothesis (CH) is indeterminate. This position is normally defended on the ground that the CH is undecidable in a way that typical axioms are not. Call this kind of undecidability “absolute undecidability”. In this paper, I seek to understand what absolute undecidability could be such that one might hope to establish that (a) CH is absolutely undecidable, (b) typical axioms are not absolutely undecidable, and (c) if a mathematical (...)
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  8. Paul J. Cohen (1966). Set Theory and the Continuum Hypothesis. New York, W. A. Benjamin.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  9. Paul J. Cohen (1963). The Independence of the Continuum Hypothesis. Proceedings of the National Academy of Sciences of the United States of America 50 (6):1143--8.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  10. Raouf Doss (1963). On Gödel's Proof That $V=L$ Implies the Generalized Continuum Hypothesis. Notre Dame Journal of Formal Logic 4 (4):283-287.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  11. Solomon Feferman, Conceptions of the Continuum.
    Key words: the continuum, structuralism, conceptual structuralism, basic structural conceptions, Euclidean geometry, Hilbertian geometry, the real number system, settheoretical conceptions, phenomenological conceptions, foundational conceptions, physical conceptions.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  12. Solomon Feferman, Conceptual Structuralism and the Continuum.
    • This comes from my general view of the nature of mathematics, that it is humanly based and that it deals with more or less clear conceptions of mathematical structures; for want of a better word, I call that view conceptual structuralism.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  13. Chris Freiling (1986). Axioms of Symmetry: Throwing Darts at the Real Number Line. Journal of Symbolic Logic 51 (1):190-200.
    We will give a simple philosophical "proof" of the negation of Cantor's continuum hypothesis (CH). (A formal proof for or against CH from the axioms of ZFC is impossible; see Cohen [1].) We will assume the axioms of ZFC together with intuitively clear axioms which are based on some intuition of Stuart Davidson and an old theorem of Sierpinski and are justified by the symmetry in a thought experiment throwing darts at the real number line. We will in fact show (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  14. Joel I. Friedman (1971). The Generalized Continuum Hypothesis is Equivalent to the Generalized Maximization Principle. Journal of Symbolic Logic 36 (1):39-54.
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  15. W. Gielen, H. de Swart & W. Veldman (1981). The Continuum Hypothesis in Intuitionism. Journal of Symbolic Logic 46 (1):121-136.
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  16. Victoria Gitman & Joel David Hamkins (2010). A Natural Model of the Multiverse Axioms. Notre Dame Journal of Formal Logic 51 (4):475-484.
    If ZFC is consistent, then the collection of countable computably saturated models of ZFC satisfies all of the Multiverse Axioms of Hamkins.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  17. Joseph Glicksohn (2004). Absorption, Hallucinations, and the Continuum Hypothesis. Behavioral and Brain Sciences 27 (6):793-794.
    The target article, in stressing the balance between neurobiological and psychological factors, makes a compelling argument in support of a continuum of perceptual and hallucinatory experience. Nevertheless, two points need to be addressed. First, the authors are probably underestimating the incidence of hallucinations in the normal population. Second, one should consider the role of absorption as a predisposing factor for hallucinations.
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  18. Kurt Gödel (1940). The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory. Princeton University Press;.
  19. Kurt Gödel (1940). The Consistency of the Continuum Hypothesis. Princeton University Press.
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  20. John Gregory (1976). Higher Souslin Trees and the Generalized Continuum Hypothesis. Journal of Symbolic Logic 41 (3):663-671.
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  21. Prentice Hall, Indeterminacy.
    It is well known that, for example, the Continuum Hypothesis can’t be proved or disproved from the standard axioms of set theory or their familiar extensions (unless those axiom systems are themselves inconsistent). Some think it follows that CH has no determinate truth value; others insist that this conclusion is false, not because there is some objective world of sets in which CH is either true or false, but on logical grounds. Claims of indeterminacy have also been made on the (...)
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  22. Joel David Hamkins (2015). Is the Dream Solution of the Continuum Hypothesis Attainable? Notre Dame Journal of Formal Logic 56 (1):135-145.
    The dream solution of the continuum hypothesis would be a solution by which we settle the continuum hypothesis on the basis of a newly discovered fundamental principle of set theory, a missing axiom, widely regarded as true. Such a dream solution would indeed be a solution, since we would all accept the new axiom along with its consequences. In this article, however, I argue that such a dream solution to $\mathrm {CH}$ is unattainable.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  23. Joel David Hamkins (2012). The Set-Theoretic Multiverse. Review of Symbolic Logic 5 (3):416-449.
    The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous range of set-theoretic possibilities, a phenomenon that challenges the universe (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  24. Kai Hauser (2002). Is Cantor's Continuum Problem Inherently Vague? Philosophia Mathematica 10 (3):257-285.
    I examine various claims to the effect that Cantor's Continuum Hypothesis and other problems of higher set theory are ill-posed questions. The analysis takes into account the viability of the underlying philosophical views and recent mathematical developments.
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  25. Jaakko Hintikka, Continuum Hypothesis as a Model-Theoretical Problem.
    Jaakko Hintikka 1. How to Study Set Theory The continuum hypothesis (CH) is crucial in the core area of set theory, viz. in the theory of the hierarchies of infinite cardinal and infinite ordinal numbers. It is crucial in that it would, if true, help to relate the two hierarchies to each other. It says that the second infinite cardinal number, which is known to be the cardinality of the first uncountable ordinal, equals the cardinality 2 o of the continuum. (...)
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  26. Peter Koellner (2010). On the Question of Absolute Undecidability. In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Philosophia Mathematica. Association for Symbolic Logic 153-188.
    The paper begins with an examination of Gödel's views on absolute undecidability and related topics in set theory. These views are sharpened and assessed in light of recent developments. It is argued that a convincing case can be made for axioms that settle many of the questions undecided by the standard axioms and that in a precise sense the program for large cardinals is a complete success “below” CH. It is also argued that there are reasonable scenarios for settling CH (...)
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  27. Donald A. Martin (2001). Multiple Universes of Sets and Indeterminate Truth Values. Topoi 20 (1):5-16.
  28. Toby Meadows (2015). Naive Infinitism: The Case for an Inconsistency Approach to Infinite Collections. Notre Dame Journal of Formal Logic 56 (1):191-212.
    This paper expands upon a way in which we might rationally doubt that there are multiple sizes of infinity. The argument draws its inspiration from recent work in the philosophy of truth and philosophy of set theory. More specifically, elements of contextualist theories of truth and multiverse accounts of set theory are brought together in an effort to make sense of Cantor’s troubling theorem. The resultant theory provides an alternative philosophical perspective on the transfinite, but has limited impact on everyday (...)
    Remove from this list | Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
1 — 50 / 111