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  1. R. Elageili & J. K. Truss (2012). Finitely Generated Free Heyting Algebras: The Well-Founded Initial Segment. Journal of Symbolic Logic 77 (4):1291-1307.
    In this paper we describe the well-founded initial segment of the free Heyting algebra α on finitely many, α, generators. We give a complete classification of initial sublattices of ₂ isomorphic to ₁ (called 'low ladders'), and prove that for 2 < α < ω, the height of the well-founded initial segment of α.
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  2. T. E. Forster & J. K. Truss (2007). Ramsey's Theorem and König's Lemma. 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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  3. T. E. Forster & J. K. Truss (2007). RamseyÔÇÖs Theorem and K├ ÂnigÔÇÖs Lemma. Archive for Mathematical Logic 46 (1):37.
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  4. J. K. Truss (2007). On Notions of Genericity and Mutual Genericity. Journal of Symbolic Logic 72 (3):755 - 766.
    Generic automorphisms of certain homogeneous structures are considered, for instance, the rationals as an ordered set, the countable universal homogeneous partial order, and the random graph. Two of these cases were discussed in [7], where it was shown that there is a generic automorphism of the second in the sense introduced in [10]. In this paper. I study various possible definitions of 'generic' and 'mutually generic', and discuss the existence of mutually generic automorphisms in some cases. In addition, generics in (...)
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  5. T. E. Forster & J. K. Truss (2003). Non-Well-Foundedness of Well-Orderable Power Sets. 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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  6. M. Giraudet & J. K. Truss (2003). Recovering Ordered Structures From Quotients of Their Automorphism Groups. Journal of Symbolic Logic 68 (4):1189-1198.
    We show that the 'tail' of a doubly homogeneous chain of countable cofinality can be recognized in the quotient of its automorphism group by the subgroup consisting of those elements whose support is bounded above. This extends the authors' earlier result establishing this for the rationals and reals. We deduce that any group is isomorphic to the outer automorphism group of some simple lattice-ordered group.
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  7. G. S. Mendick & J. K. Truss (2003). A Notion of Rank in Set Theory Without Choice. Archive for Mathematical Logic 42 (2):165-178.
    Starting from the definition of `amorphous set' in set theory without the axiom of choice, we propose a notion of rank (which will only make sense for, at most, the class of Dedekind finite sets), which is intended to be an analogue in this situation of Morley rank in model theory.
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  8. P. Creed & J. K. Truss (2001). On Quasi-Amorphous Sets. Archive for Mathematical Logic 40 (8):581-596.
    A set is said to be amorphous if it is infinite, but cannot be written as the disjoint union of two infinite sets. The possible structures which an amorphous set can carry were discussed in [5]. Here we study an analogous notion at the next level up, that is to say replacing finite/infinite by countable/uncountable, saying that a set is quasi-amorphous if it is uncountable, but is not the disjoint union of two uncountable sets, and every infinite subset has a (...)
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  9. A. S. Morozov & J. K. Truss (2001). On Computable Automorphisms of the Rational Numbers. Journal of Symbolic Logic 66 (3):1458-1470.
    The relationship between ideals I of Turing degrees and groups of I-recursive automorphisms of the ordering on rationals is studied. We discuss the differences between such groups and the group of all automorphisms, prove that the isomorphism type of such a group completely defines the ideal I, and outline a general correspondence between principal ideals of Turing degrees and the first-order properties of such groups.
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  10. P. Creed & J. K. Truss (2000). On -Amorphous Sets. Annals of Pure and Applied Logic 101 (2-3):185-226.
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  11. B. Herwig, H. D. Macpherson, G. Martin, A. Nurtazin & J. K. Truss (2000). On aleph0. Annals of Pure and Applied Logic 101 (1):65-94.
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  12. S. B. Cooper & J. K. Truss (eds.) (1999). Models and Computability: Invited Papers From Logic Colloquium '97, European Meeting of the Association for Symbolic Logic, Leeds, July 1997. Cambridge University Press.
    Together, Models and Computability and its sister volume Sets and Proofs will provide readers with a comprehensive guide to the current state of mathematical logic. All the authors are leaders in their fields and are drawn from the invited speakers at 'Logic Colloquium '97' (the major international meeting of the Association of Symbolic Logic). It is expected that the breadth and timeliness of these two volumes will prove an invaluable and unique resource for specialists, post-graduate researchers, and the informed and (...)
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  13. U. Felgner & J. K. Truss (1999). The Independence of the Prime Ideal Theorem From the Order-Extension Principle. Journal of Symbolic Logic 64 (1):199-215.
    It is shown that the boolean prime ideal theorem BPIT: every boolean algebra has a prime ideal, does not follow from the order-extension principle OE: every partial ordering can be extended to a linear ordering. The proof uses a Fraenkel-Mostowski model, where the family of atoms is indexed by a countable universal-homogeneous boolean algebra whose boolean partial ordering has a `generic' extension to a linear ordering. To illustrate the technique for proving that the order-extension principle holds in the model we (...)
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  14. B. Herwig, H. D. Macpherson, G. Martin, A. Nurtazin & J. K. Truss (1999). On -Categorical Weakly -Minimal Structures. Annals of Pure and Applied Logic 101 (1):65-93.
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  15. B. Herwig, H. D. Macpherson, G. Martin, A. Nurtazin & J. K. Truss (1999). On ℵ0-Categorical Weakly o-Minimal Structures. Annals of Pure and Applied Logic 101 (1):65-93.
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  16. S. Shelah & J. K. Truss (1999). On Distinguishing Quotients of Symmetric Groups. Annals of Pure and Applied Logic 97 (1-3):47-83.
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  17. M. Hyland Hodges, A. H. Lachlan, A. Louveau, Y. N. Moschovakis, L. Pacholski, A. B. Slomson, J. K. Truss & S. S. Wainer (1998). 1997 European Summer Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 4 (1).
     
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  18. J. K. Truss (1995). The Structure of Amorphous Sets. Annals of Pure and Applied Logic 73 (2):191-233.
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  19. J. K. Truss (1984). Cancellation Laws for Surjective Cardinals. Annals of Pure and Applied Logic 27 (2):165-208.
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  20. J. K. Truss (1983). The Noncommutativity of Random and Generic Extensions. Journal of Symbolic Logic 48 (4):1008-1012.
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