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  1. Uri Abraham (1983). On Forcing Without the Continuum Hypothesis. Journal of Symbolic Logic 48 (3):658-661.
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  2. C. Alvarez Jimenez (1995). Some Logical Remarks Concerning the Continuum Problem. Boston Studies in the Philosophy of Science 172:173-186.
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  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.
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  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 (...)
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  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.
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  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.
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  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 (...)
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  8. Paul J. Cohen (1966). Set Theory and the Continuum Hypothesis. New York, W. A. Benjamin.
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  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.
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  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.
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  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.
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  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.
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  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 (...)
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  14. Joel I. Friedman (1971). The Generalized Continuum Hypothesis is Equivalent to the Generalized Maximization Principle. Journal of Symbolic Logic 36 (1):39-54.
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  15. W. Gielen, H. de Swart & W. Veldman (1981). The Continuum Hypothesis in Intuitionism. Journal of Symbolic Logic 46 (1):121-136.
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  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.
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  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.
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  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.
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  20. John Gregory (1976). Higher Souslin Trees and the Generalized Continuum Hypothesis. Journal of Symbolic Logic 41 (3):663-671.
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  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 (...)
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  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.
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  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 (...)
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  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.
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  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. (...)
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  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 (...)
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  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 (...)
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  29. Kannan Nambiar, Generalized Continuum Hypothesis and the Axiom of Combinatorial Sets.
    Axiom of Combinatorial Sets is defined and used to derive Generalized Continuum Hypothesis.
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  30. George C. Nelson (1998). Preservation Theorems Without Continuum Hypothesis. Studia Logica 60 (3):343-355.
    Many results concerning the equivalence between a syntactic form of formulas and a model theoretic conditions are proven directly without using any form of a continuum hypothesis. In particular, it is demonstrated that any reduced product sentence is equivalent to a Horn sentence. Moreover, in any first order language without equality one now has that a reduced product sentence is equivalent to a Horn sentence and any sentence is equivalent to a Boolean combination of Horn sentences.
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  31. Anne Newstead & Franklin James (2008). On the Reality of the Continuum. Philosophy 83 (01):117-28.
    In a recent article (‘The Continuum: Russell’s Moment of Candour’), Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of study. (...)
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  32. Richard A. Platek (1969). Eliminating the Continuum Hypothesis. Journal of Symbolic Logic 34 (2):219-225.
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  33. Assaf Rinot (2010). The Search for Diamonds: Review of S. Shelah, Middle Diamond; S. Shelah, Diamonds; and M. Zeman, Diamond, GCH and Weak Square. [REVIEW] Bulletin of Symbolic Logic 16 (3):420 - 423.
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  34. Rolf Schock (1977). A Note on the Axiom of Choice and the Continuum Hypothesis. Notre Dame Journal of Formal Logic 18 (3):409-414.
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  35. Rolf Schock (1966). A Simple Version of the Generalized Continuum Hypothesis. Notre Dame Journal of Formal Logic 7 (3):287-288.
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  36. Boleslaw Sobocinski (1963). A Note On The Generalized Continuum Hypothesis, Ii. Notre Dame Journal of Formal Logic 4 (1):67-79.
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  37. Bolesław Sobociński (1963). A Note on the Generalized Continuum Hypothesis. III. Notre Dame Journal of Formal Logic 4 (3):233-240.
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  38. Bolesław Sobociński (1963). A Note on the Generalized Continuum Hypothesis. II. Notre Dame Journal of Formal Logic 4 (1):67-79.
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  39. Bolesław Sobociński (1962). A Note on the Generalized Continuum Hypothesis. I. Notre Dame Journal of Formal Logic 3 (4):274-278.
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  40. Thomas Weston (1976). Kreisel, the Continuum Hypothesis and Second Order Set Theory. Journal of Philosophical Logic 5 (2):281 - 298.
    The major point of contention among the philosophers and mathematicians who have written about the independence results for the continuum hypothesis (CH) and related questions in set theory has been the question of whether these results give reason to doubt that the independent statements have definite truth values. This paper concerns the views of G. Kreisel, who gives arguments based on second order logic that the CH does have a truth value. The view defended here is that although Kreisel's conclusion (...)
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  41. Thomas S. Weston (1977). The Continuum Hypothesis is Independent of Second-Order ZF. Notre Dame Journal of Formal Logic 18 (3):499-503.
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