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  1.  30
    A Note on Freedom From Detachment in the Logic of Paradox.Jc Beall, Thomas Forster & Jeremy Seligman - 2013 - Notre Dame Journal of Formal Logic 54 (1):15-20.
    We shed light on an old problem by showing that the logic LP cannot define a binary connective $\odot$ obeying detachment in the sense that every valuation satisfying $\varphi$ and $(\varphi\odot\psi)$ also satisfies $\psi$ , except trivially. We derive this as a corollary of a more general result concerning variable sharing.
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  2. The Iterative Conception of Set.Thomas Forster - 2008 - Review of Symbolic Logic 1 (1):97-110.
    The phrase ‘The iterative conception of sets’ conjures up a picture of a particular settheoretic universe – the cumulative hierarchy – and the constant conjunction of phrasewith-picture is so reliable that people tend to think that the cumulative hierarchy is all there is to the iterative conception of sets: if you conceive sets iteratively, then the result is the cumulative hierarchy. In this paper, I shall be arguing that this is a mistake: the iterative conception of set is a good (...)
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  3.  3
    Decidable Fragments of the Simple Theory of Types with Infinity and $Mathrm{NF}$.Anuj Dawar, Thomas Forster & Zachiri McKenzie - 2017 - Notre Dame Journal of Formal Logic 58 (3):433-451.
    We identify complete fragments of the simple theory of types with infinity and Quine’s new foundations set theory. We show that TSTI decides every sentence ϕ in the language of type theory that is in one of the following forms: ϕ=∀x1r1⋯∀xkrk∃y1s1⋯∃ylslθ where the superscripts denote the types of the variables, s1>⋯>sl, and θ is quantifier-free, ϕ=∀x1r1⋯∀xkrk∃y1s⋯∃ylsθ where the superscripts denote the types of the variables and θ is quantifier-free. This shows that NF decides every stratified sentence ϕ in the language (...)
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  4.  16
    Mathematical Objects Arising From Equivalence Relations and Their Implementation in Quine's NF.Thomas Forster - 2016 - Philosophia Mathematica 24 (1):nku005.
    Many mathematical objects arise from equivalence classes and invite implementation as those classes. Set-existence principles that would enable this are incompatible with ZFC's unrestricted aussonderung but there are set theories which admit more instances than does ZF. NF provides equivalence classes for stratified relations only. Church's construction provides equivalence classes for “low” sets, and thus, for example, a set of all ordinals. However, that set has an ordinal in turn which is not a member of the set constructed; so no (...)
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  5.  5
    Mathematical Objects Arising From Equivalence Relations and Their Implementation in Quine's NF.Thomas Forster - 2016 - Philosophia Mathematica 24 (1):50-59.
    Many mathematical objects arise from equivalence classes and invite implementation as those classes. Set-existence principles that would enable this are incompatible with ZFC's unrestricted _aussonderung_ but there are set theories which admit more instances than does ZF. NF provides equivalence classes for stratified relations only. Church's construction provides equivalence classes for "low" sets, and thus, for example, a set of all ordinals. However, that set has an ordinal in turn which is not a member of the set constructed; so no (...)
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  6. ZF + "Every Set is the Same Size as a Wellfounded Set".Thomas Forster - 2003 - Journal of Symbolic Logic 68 (1):1-4.
    Let ZFB be ZF + "every set is the same size as a wellfounded set". Then the following are true. Every sentence true in every (Rieger-Bernays) permutation model of a model of ZF is a theorem of ZFB. (i.e.. ZFB is the theory of Rieger-Bernays permutation models of models of ZF) ZF and ZFAFA are both extensions of ZFB conservative for stratified formulæ. The class of models of ZFB is closed under creation of Rieger-Bernays permutation models.
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  7.  79
    Yablo's Paradox and the Omitting Types Theorem for Propositional Languages.Thomas Forster - 2011 - Logique Et Analyse 54 (215):323.
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  8.  3
    Permutations and Wellfoundedness: The True Meaning of the Bizarre Arithmetic of Quine's NF.Thomas Forster - 2006 - Journal of Symbolic Logic 71 (1):227 - 240.
    It is shown that, according to NF, many of the assertions of ordinal arithmetic involving the T-function which is peculiar to NF turn out to be equivalent to the truth-in-certain-permutation-models of assertions which have perfectly sensible ZF-style meanings, such as: the existence of wellfounded sets of great size or rank, or the nonexistence of small counterexamples to the wellfoundedness of ∈. Everything here holds also for NFU if the permutations are taken to fix all urelemente.
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  9.  16
    Permutations and Stratified Formulae a Preservation Theorem.Thomas Forster - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (5):385-388.
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  10.  12
    End-Extensions Preserving Power Set.Thomas Forster & Richard Kaye - 1991 - Journal of Symbolic Logic 56 (1):323-328.
  11.  37
    NF at (Nearly) 75.Thomas Forster - 2010 - Logique Et Analyse 53 (212):483.
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  12.  11
    Ramsey's Theorem and König's Lemma.T. E. Forster & J. K. Truss - 2007 - Archive for Mathematical Logic 46 (1):37-42.
    We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice.
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  13.  16
    Permutation Models in the Sense of Rieger-Bernays.T. E. Forster - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (3):201-210.
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  14.  10
    Finite-to-One Maps.Thomas Forster - 2003 - Journal of Symbolic Logic 68 (4):1251-1253.
    It is shown in ZF (without choice) that if there is a finite-to-one map P(X) → X, then X is finite.
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  15.  52
    An Order-Theoretic Account of Some Set-Theoretic Paradoxes.Thomas Forster & Thierry Libert - 2011 - Notre Dame Journal of Formal Logic 52 (1):1-19.
    We present an order-theoretic analysis of set-theoretic paradoxes. This analysis will show that a large variety of purely set-theoretic paradoxes (including the various Russell paradoxes as well as all the familiar implementations of the paradoxes of Mirimanoff and Burali-Forti) are all instances of a single limitative phenomenon.
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  16.  1
    Permutations and Stratified Formulae a Preservation Theorem.Thomas Forster - 1990 - Mathematical Logic Quarterly 36 (5):385-388.
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  17.  16
    A Consistent Higher-Order Theory Without a Model.Thomas Forster - 1989 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (5):385-386.
  18.  26
    Implementing Mathematical Objects in Set Theory.Thomas Forster - 2007 - Logique Et Analyse 50 (197):79-86.
    In general little thought is given to the general question of how to implement mathematical objects in set theory. It is clear that—at various times in the past—people have gone to considerable lengths to devise implementations with nice properties. There is a litera- ture on the evolution of the Wiener-Kuratowski ordered pair, and a discussion by Quine of the merits of an ordered-pair implemen- tation that makes every set an ordered pair. The implementation of ordinals as Von Neumann ordinals is (...)
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  19.  9
    Term Models for Weak Set Theories with a Universal Set.T. E. Forster - 1987 - Journal of Symbolic Logic 52 (2):374-387.
  20.  15
    The Status of the Axiom of Choice in Set Theory with a Universal Set.T. E. Forster - 1985 - Journal of Symbolic Logic 50 (3):701-707.
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  21.  2
    Permutation Models in the Sense of Rieger‐Bernays.T. E. Forster - 1987 - Mathematical Logic Quarterly 33 (3):201-210.
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  22.  7
    Further Consistency and Independence Results in NF Obtained by the Permutation Method.T. E. Forster - 1983 - Journal of Symbolic Logic 48 (2):236-238.
  23.  12
    Normal Subgroups of Infinite Symmetric Groups, with an Application to Stratified Set Theory.Nathan Bowler & Thomas Forster - 2009 - Journal of Symbolic Logic 74 (1):17-26.
  24.  13
    Sharvy's Lucy and Benjamin Puzzle.Thomas Forster - 2008 - Studia Logica 90 (2):249 - 256.
    Sharvy’s puzzle concerns a situation in which common knowledge of two parties is obtained by repeated observation each of the other, no fixed point being reached in finite time. Can a fixed point be reached?
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  25.  6
    Alternative Set Theories.Thierry Libert, T. Forster, R. Holmes, Dov M. Gabbay, John Woods & Akihiro Kanamori - 2009 - In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier.
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  26.  10
    Quine's New Foundations.Thomas Forster - 1985 - Journal of Symbolic Logic.
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  27.  9
    Non-Well-Foundedness of Well-Orderable Power Sets.T. E. Forster & J. K. Truss - 2003 - Journal of Symbolic Logic 68 (3):879-884.
    Tarski [5] showed that for any set X, its set w(X) of well-orderable subsets has cardinality strictly greater than that of X, even in the absence of the axiom of choice. We construct a Fraenkel-Mostowski model in which there is an infinite strictly descending sequence under the relation |w (X)| = |Y|. This contrasts with the corresponding situation for power sets, where use of Hartogs' ℵ-function easily establishes that there can be no infinite descending sequence under the relation |P(X)| = (...)
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  28.  4
    Erdös-Rado Without Choice.Thomas Forster - 2007 - Journal of Symbolic Logic 72 (3):897 - 900.
    A version of the Erdös-Rado theorem on partitions of the unordered n-tuples from uncountable sets is proved, without using the axiom of choice. The case with exponent 1 is just the Sierpinski-Hartogs' result that $\aleph (\alpha)\leq 2^{2^{2^{\alpha}}}$.
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  29.  2
    Sharvy’s Lucy and Benjamin Puzzle.Thomas Forster - 2008 - Studia Logica 90 (2):249-256.
    Sharvy's puzzle concerns a situation in which common knowledge of two parties is obtained by repeated observation each of the other, no fixed point being reached in finite time. Can a fixed point be reached?
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  30.  2
    A Consistent Higher‐Order Theory Without a (Higher‐Order) Model.Thomas Forster - 1989 - Mathematical Logic Quarterly 35 (5):385-386.
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  31. Original Letters of Locke; Algernon Sidney; and Anthony, Lord Shaftesbury, Author of the"Characteristics". With an Analytical Sketch of the Writings and Opinions of Locke and Other Metaphysicians.T. Forster, John Locke, Algernon Sidney & Anthony Ashley Cooper Shaftesbury - 1830 - J.B. Nichols and Son.
     
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  32.  12
    Reasoning About Theoretical Entities.T. E. Forster - 2003 - World Scientific.
    As such this book fills a void in the philosophical literature and presents a challenge to every would-be (anti-)reductionist.
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  33. Rhetorical Devices in Analytic Philosophy.Thomas Forster - 2010 - Logique Et Analyse 53 (210):93.
     
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  34. RamseyÔÇÖs Theorem and K├ ÂnigÔÇÖs Lemma.T. E. Forster & J. K. Truss - 2007 - Archive for Mathematical Logic 46 (1):37.
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  35. Original Letters of John Locke, Alg. Sidney, and Lord Shaftesbury with an Analytical Sketch of the Writings and Opinions of Locke and Other Metaphysicians.John Locke, T. Forster, Anthony Ashley Cooper Shaftesbury & Algernon Sidney - 1847 - Privately Printed.