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J. K. Truss [24]John K. Truss [5]John Truss [4]J. Truss [2]
J. . K. Truss [1]John Kenneth Truss [1]
  1.  18
    The Structure of Amorphous Sets.J. K. Truss - 1995 - Annals of Pure and Applied Logic 73 (2):191-233.
    A set is said to be amorphous if it is infinite, but is not the disjoint union of two infinite subsets. Thus amorphous sets can exist only if the axiom of choice is false. We give a general study of the structure which an amorphous set can carry, with the object of eventually obtaining a complete classification. The principal types of amorphous set we distinguish are the following: amorphous sets not of projective type, either bounded or unbounded size of members (...)
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  2.  28
    On ℵ0-Categorical Weakly o-Minimal Structures.B. Herwig, H. D. Macpherson, G. Martin, A. Nurtazin & J. K. Truss - 1999 - Annals of Pure and Applied Logic 101 (1):65-93.
    0-categorical o-minimal structures were completely described by Pillay and Steinhorn 565–592), and are essentially built up from copies of the rationals as an ordered set by ‘cutting and copying’. Here we investigate the possible structures which an 0-categorical weakly o-minimal set may carry, and find that there are some rather more interesting examples. We show that even here the possibilities are limited. We subdivide our study into the following principal cases: the structure is 1-indiscernible, in which case all possibilities are (...)
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  3.  6
    Ehrenfeucht–Fraïssé Games on Ordinals.F. Mwesigye & J. K. Truss - 2018 - Annals of Pure and Applied Logic 169 (7):616-636.
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  4.  33
    On o-Amorphous Sets.P. Creed & J. K. Truss - 2000 - Annals of Pure and Applied Logic 101 (2-3):185-226.
    We study a notion of ‘o-amorphous’ which bears the same relationship to ‘o-minimal’ as ‘amorphous’ 191–233) does to ‘strongly minimal’. A linearly ordered set is said to be o-amorphous if its only subsets are finite unions of intervals. This turns out to be a relatively straightforward case, and we can provide a complete ‘classification’, subject to the same provisos as in Truss . The reason is that since o-amorphous is an essentially second-order notion, it corresponds more accurately to 0-categorical o-minimal, (...)
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  5.  81
    On Quasi-Amorphous Sets.P. Creed & J. K. Truss - 2001 - 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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  6.  19
    Reconstructing the Topology on Monoids and Polymorphism Clones of the Rationals.Mike Behrisch, John K. Truss & Edith Vargas-García - 2017 - Studia Logica 105 (1):65-91.
    We show how to reconstruct the topology on the monoid of endomorphisms of the rational numbers under the strict or reflexive order relation, and the polymorphism clone of the rational numbers under the reflexive relation. In addition we show how automatic homeomorphicity results can be lifted to polymorphism clones generated by monoids.
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  7.  53
    A Notion of Rank in Set Theory Without Choice.G. S. Mendick & J. K. Truss - 2003 - 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.  20
    Finitely Generated Free Heyting Algebras: The Well-Founded Initial Segment.R. Elageili & J. K. Truss - 2012 - 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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  9.  11
    The Well‐Ordered and Well‐Orderable Subsets of a Set.John Truss - 1973 - Mathematical Logic Quarterly 19 (14‐18):211-214.
  10. The Independence of the Prime Ideal Theorem From the Order-Extension Principle.U. Felgner & J. K. Truss - 1999 - 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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  11. The Noncommutativity of Random and Generic Extensions.J. K. Truss - 1983 - Journal of Symbolic Logic 48 (4):1008-1012.
  12.  28
    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.  20
    On Notions of Genericity and Mutual Genericity.J. K. Truss - 2007 - 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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  14. On aleph0.B. Herwig, H. D. Macpherson, G. Martin, A. Nurtazin & J. K. Truss - 1999 - Annals of Pure and Applied Logic 101 (1):65-94.
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  15.  48
    On Computable Automorphisms of the Rational Numbers.A. S. Morozov & J. K. Truss - 2001 - 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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  16.  21
    Countably Categorical Coloured Linear Orders.Feresiano Mwesigye & John K. Truss - 2010 - Mathematical Logic Quarterly 56 (2):159-163.
    In this paper, we give a classification of ℵ0-categorical coloured linear orders, generalizing Rosenstein's characterization of ℵ0-categorical linear orderings. We show that they can all be built from coloured singletons by concatenation and ℚn-combinations . We give a method using coding trees to describe all structures in our list.
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  17.  23
    Models and Computability: Invited Papers From Logic Colloquium '97, European Meeting of the Association for Symbolic Logic, Leeds, July 1997.S. B. Cooper & J. K. Truss (eds.) - 1999 - 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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  18. Logic Colloquium '86.F. R. Drake & J. K. Truss - 1988
  19. The 1996-97 ASL Winter Meeting Will Be Held in Conjunction with the Annual Meeting of the American Mathematical Society During January 8-11, 1997, in San Diego, California. The 1996-97 ASL Annual Meeting Will Be Held March 22-25, 1997, at the Massachusetts Institute of Technology in Cambridge, Massachusetts. Chair of the Local Organizing Com-Mittee is Sy Friedman. [REVIEW]A. Louveau, Y. Moschovakis, L. Pacholski, H. Schwichtenberg, T. Slaman, J. Truss, H. D. Macpherson, A. Slomson & S. Wainer - 1996 - Bulletin of Symbolic Logic 2:121.
  20.  24
    Recovering Ordered Structures From Quotients of Their Automorphism Groups.M. Giraudet & J. K. Truss - 2003 - 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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  21.  12
    The American Mathematical Society During January 8–11, 1997, in San Diego, California.• The 1996–97 ASL Annual Meeting Will Be Held March 22–25, 1997, at the Massachusetts Institute of Technology in Cambridge, Massachusetts. Chair of the Local Organizing Com-Mittee is Sy Friedman.• The 1997 ASL European Summer Meeting (Logic Colloquium'97) Will Be Held in Early. [REVIEW]J. Derrick, F. Drake, D. Macpherson, A. Slomson, J. Truss & S. Wainer - 1995 - Bulletin of Symbolic Logic 1 (3).
  22.  4
    Ehrenfeucht-Fraïssé Games on a Class of Scattered Linear Orders.Feresiano Mwesigye & John Kenneth Truss - 2020 - Journal of Symbolic Logic 85 (1):37-60.
    Two structures A and B are n-equivalent if Player II has a winning strategy in the n-move Ehrenfeucht-Fraïssé game on A and B. In earlier articles we studied n-equivalence classes of ordinals and coloured ordinals. In this article we similarly treat a class of scattered order-types, focussing on monomials and sums of monomials in ω and its reverse ω*.
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  23. Sets and Proofs.S. Barry Cooper & John K. Truss - 2001 - Studia Logica 69 (3):446-448.
  24. Logic Colloquium '86.F. R. Drake & J. K. Truss - 1989 - Studia Logica 48 (3):396-400.
     
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  25.  7
    RamseyÔÇÖs Theorem and K├ ÂnigÔÇÖs Lemma.T. E. Forster & J. K. Truss - 2007 - Archive for Mathematical Logic 46 (1):37.
    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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  26.  8
    On Distinguishing Quotients of Symmetric Groups.S. Shelah & J. K. Truss - 1999 - Annals of Pure and Applied Logic 97 (1-3):47-83.
    A study of the elementary theory of quotients of symmetric groups is carried out in a similar spirit to Shelah . Apart from the trivial and alternating subgroups, the normal subgroups of the full symmetric group S on an infinite cardinal μ are all of the form Sκ = the subgroup consisting of elements whose support has cardinality 20, cƒ 20 < κ, 0 < κ < 20, and κ = 0, we make a further analysis of the first order (...)
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  27.  2
    Surjectively Rigid Chains.Mayra Montalvo-Ballesteros & John K. Truss - 2020 - Mathematical Logic Quarterly 66 (4):466-478.
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  28.  7
    On Certain Arbitrarily Long Sequences of Cardinals.John Truss - 1973 - Mathematical Logic Quarterly 19 (14‐18):209-210.
  29.  8
    Cancellation Laws for Surjective Cardinals.J. K. Truss - 1984 - Annals of Pure and Applied Logic 27 (2):165-208.
  30.  4
    1997 European Summer Meeting of the Association for Symbolic Logic.M. Hyland Hodges, A. H. Lachlan, A. Louveau, Y. N. Moschovakis, L. Pacholski, A. B. Slomson, J. K. Truss & S. S. Wainer - 1998 - Bulletin of Symbolic Logic 4 (1):55-117.
  31.  13
    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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  32.  1
    Interpreting the Weak Monadic Second Order Theory of the Ordered Rationals.John K. Truss - 2022 - Mathematical Logic Quarterly 68 (1):74-78.
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