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  1. Ludwik Borkowski (1958). Reduction of Arithmetic to Logic Based on the Theory of Types Without the Axiom of Infinity and the Typical Ambiguity of Arithmetical Constants. Studia Logica 8 (1):283 - 297.
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  2. 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? (...)
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  3. 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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  4. Herbert Hochberg (1977). Properties, Abstracts, and the Axiom of Infinity. Journal of Philosophical Logic 6 (1):193 - 207.
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  5. Claus Janew (2014). Dialogue on Alternating Consciousness: From Perception to Infinities and Back to Free Will. Journal of Consciousness Exploration and Research 5 (4):351-391.
    Can we trace back consciousness, reality, awareness, and free will to a single basic structure without giving up any of them? Can the universe exist in both real and individual ways without being composed of both? This dialogue founds consciousness and freedom of choice on the basis of a new reality concept that also includes the infinite as far as we understand it. Just the simplest distinction contains consciousness. It is not static, but a constant alternation of perspectives. From its (...)
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  6. Antonio Leon, Hilbert's Machine and the Axiom of Infinity.
    Hilbert's machine is a supertask machine inspired by Hilbert's Hotel whose functioning leads to a contradiction that compromises the Axiom of Infinity.
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  7. M. Potter (1996). Taming the Infinite. [REVIEW] British Journal for the Philosophy of Science 47 (4):609-619.
    A critique of Shaughan Lavine's attempt in /Understanding the Infinite/ to reduce talk about the infinite to finitely comprehensible terms.
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  8. W. V. Quine (1953). On Ω-Inconsistency and a so-Called Axiom of Infinity. Journal of Symbolic Logic 18 (2):119-124.
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  9. J. Barkley Rosser (1952). The Axiom of Infinity in Quine's New Foundations. Journal of Symbolic Logic 17 (4):238-242.
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  10. Kip Sewell, The Case Against Infinity.
    Infinity and infinite sets, as traditionally defined in mathematics, are shown to be logical absurdities. To maintain logical consistency, mathematics ought to abandon the traditional notion of infinity. It is proposed that infinity should be replaced with the concept of “indefiniteness”. This further implies that other fields drawing on mathematics, such as physics and cosmology, ought to reject theories that postulate infinities of space and time. It is concluded that however indefinite our calculations of space and time become, the Universe (...)
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