15 found
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  1.  43
    Happy Families.A. R. D. Mathias - 1977 - Annals of Pure and Applied Logic 12 (1):59.
  2.  19
    The Strength of Mac Lane Set Theory.A. R. D. Mathias - 2001 - Annals of Pure and Applied Logic 110 (1-3):107-234.
    Saunders Mac Lane has drawn attention many times, particularly in his book Mathematics: Form and Function, to the system of set theory of which the axioms are Extensionality, Null Set, Pairing, Union, Infinity, Power Set, Restricted Separation, Foundation, and Choice, to which system, afforced by the principle, , of Transitive Containment, we shall refer as . His system is naturally related to systems derived from topos-theoretic notions concerning the category of sets, and is, as Mac Lane emphasises, one that is (...)
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  3.  24
    Slim Models of Zermelo Set Theory.A. R. D. Mathias - 2001 - Journal of Symbolic Logic 66 (2):487-496.
    Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula Φ(λ, a) such that for any sequence $\langle A_{\lambda} \mid \lambda \text{a limit ordinal} \rangle$ where for each $\lambda, A_{\lambda} \subseteq ^{\lambda}2$ , there is a supertransitive inner model of Zermelo containing all ordinals in which for every λ A (...)
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  4.  27
    Mengenlehre, Edited by Ulrich Feigner, Wissenschaftliche Buchgesellschaft, Darmstadt1979, Vii + 331 Pp. [REVIEW]A. R. D. Mathias - 1991 - Journal of Symbolic Logic 56 (1):345-348.
  5.  17
    A Note on the Schemes of Replacement and Collection.A. R. D. Mathias - 2007 - Archive for Mathematical Logic 46 (1):43-50.
    We derive the schemes of from certain weak forms of the same.
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  6.  31
    A Term of Length 4 523 659 424 929.A. R. D. Mathias - 2002 - Synthese 133 (1-2):75 - 86.
    Bourbaki suggest that their definition of the number 1 runs to some tens of thousands of symbols. We show that that is a considerable under-estimate, the true number of symbols being that in the title, not counting 1 179 618 517 981 links between symbols that are needed to disambiguate the whole expression.
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  7.  64
    On the Existence of Large P-Ideals.Winfried Just, A. R. D. Mathias, Karel Prikry & Petr Simon - 1990 - Journal of Symbolic Logic 55 (2):457-465.
    We prove the existence of p-ideals that are nonmeagre subsets of P(ω) under various set-theoretic assumptions.
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  8.  12
    A Term of Length 4 523 659 424 929.A. R. D. Mathias - 2002 - Synthese 133 (1):75-86.
    Bourbaki suggest that their definition of the number 1 runs to some tens of thousands of symbols. We show that that is a considerable under-estimate, the true number of symbols being that in the title, not counting 1 179 618 517 981 links between symbols that are needed to disambiguate the whole expression.
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  9.  7
    Slim Models of Zermelo Set Theory.A. R. D. Mathias - 2001 - Journal of Symbolic Logic 66 (2):487-496.
    Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula $\Phi$ such that for any sequence $\langle A_{\lambda} \mid \lambda \text{a limit ordinal} \rangle$ where for each $\lambda, A_{\lambda} \subseteq ^{\lambda}2$, there is a supertransitive inner model of Zermelo containing all ordinals in which for every $\lambda A_{\lambda} = \{\alpha (...)
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  10.  12
    Descriptive Set Theory in L Ω 1 Ω.Robert Vaught, A. R. D. Mathias & H. Rogers - 1982 - Journal of Symbolic Logic 47 (1):217-218.
  11.  16
    Rudimentary Recursion, Gentle Functions and Provident Sets.A. R. D. Mathias & N. J. Bowler - 2015 - Notre Dame Journal of Formal Logic 56 (1):3-60.
    This paper, a contribution to “micro set theory”, is the study promised by the first author in [M4], as improved and extended by work of the second. We use the rudimentarily recursive functions and the slightly larger collection of gentle functions to initiate the study of provident sets, which are transitive models of $\mathsf{PROVI}$, a subsystem of $\mathsf{KP}$ whose minimal model is Jensen’s $J_{\omega}$. $\mathsf{PROVI}$ supports familiar definitions, such as rank, transitive closure and ordinal addition—though not ordinal multiplication—and Shoenfield’s unramified (...)
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  12.  5
    Review: Ulrich Felgner, Mengenlehre. [REVIEW]A. R. D. Mathias - 1991 - Journal of Symbolic Logic 56 (1):345-348.
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  13. Set Theory: Techniques and Applications.Carlos Augusto Di Prisco, Jean A. Larson, Joan Bagaria & A. R. D. Mathias - 2000 - Studia Logica 66 (3):426-428.
  14. Cambridge Summer School in Mathematical Logic.A. R. D. Mathias & H. Rogers (eds.) - 1973 - New York: Springer Verlag.
  15. Cambridge Summer School in Mathematical Logic Held in Cambridge/England, August 1-21, 1971.A. R. D. Mathias & H. Rogers - 1973
     
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