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  1. B. Abbott & L. Hauser, Realism, Model Theory, and Linguistic Semantics.
    George Lakoff (in his book Women, Fire, and Dangerous Things(1987) and the paper "Cognitive semantics" (1988)) champions some radical foundational views. Strikingly, Lakoff opposes realism as a metaphysical position, favoring instead some supposedly mild form of idealism such as that recently espoused by Hilary Putnam, going under the name "internal realism." For what he takes to be connected reasons, Lakoff also rejects truth conditional model-theoretic semantics for natural language. This paper examines an argument, given by Lakoff, against realism and MTS. (...)
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  2. Alexander Abian (1975). On the Use of More Than Two-Element Boolean Valued Models. Notre Dame Journal of Formal Logic 16 (4):555-564.
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  3. Alexander Abian (1974). Nonstandard Models for Arithmetic and Analysis. Studia Logica 33 (1):11 - 22.
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  4. Fred G. Abramson (1981). Locally Countable Models of Σ1-Separation. Journal of Symbolic Logic 46 (1):96 - 100.
    Let α be any countable admissible ordinal greater than ω. There is a transitive set A such that A is admissible, locally countable, On A = α, and A satisfies Σ 1 -separation. In fact, if B is any nonstandard model of $KP + \forall x \subseteq \omega$ (the hyperjump of x exists), the ordinal standard part of B is greater than ω, and every standard ordinal in B is countable in B, then HC B ∩ (standard part of B) (...)
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  5. Fred G. Abramson (1979). Σ1-Separation. Journal of Symbolic Logic 44 (3):374 - 382.
    Let A be a standard transitive admissible set. Σ 1 -separation is the principle that whenever X and Y are disjoint Σ A 1 subsets of A then there is a Δ A 1 subset S of A such that $X \subseteq S$ and $Y \cap S = \varnothing$ . Theorem. If A satisfies Σ 1 -separation, then (1) If $\langle T_n\mid n is a sequence of trees on ω each of which has at most finitely many infinite paths in (...)
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  6. Fred G. Abramson & Leo A. Harrington (1978). Models Without Indiscernibles. Journal of Symbolic Logic 43 (3):572-600.
    For T any completion of Peano Arithmetic and for n any positive integer, there is a model of T of size $\beth_n$ with no (n + 1)-length sequence of indiscernibles. Hence the Hanf number for omitting types over T, H(T), is at least $\beth_\omega$ . (Now, using an upper bound previously obtained by Julia Knight H (true arithmetic) is exactly $\beth_\omega$ ). If T ≠ true arithmetic, then $H(T) = \beth_{\omega1}$ . If $\delta \not\rightarrow (\rho)^{ , then any completion of (...)
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  7. J. Adámek, P. T. Johnstone, J. A. Makowsky & J. Rosický (1997). Finitary Sketches. Journal of Symbolic Logic 62 (3):699-707.
    Finitary sketches, i.e., sketches with finite-limit and finite-colimit specifications, are proved to be as strong as geometric sketches, i.e., sketches with finite-limit and arbitrary colimit specifications. Categories sketchable by such sketches are fully characterized in the infinitary first-order logic: they are axiomatizable by σ-coherent theories, i.e., basic theories using finite conjunctions, countable disjunctions, and finite quantifications. The latter result is absolute; the equivalence of geometric and finitary sketches requires (in fact, is equivalent to) the non-existence of measurable cardinals.
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  8. Jiří Adámek (2004). On Quasivarieties and Varieties as Categories. Studia Logica 78 (1-2):7 - 33.
    Finitary quasivarieties are characterized categorically by the existence of colimits and of an abstractly finite, regularly projective regular generator G. Analogously, infinitary quasivarieties are characterized: one drops the assumption that G be abstractly finite. For (finitary) varieties the characterization is similar: the regular generator is assumed to be exactly projective, i.e., hom(G, –) is an exact functor. These results sharpen the classical characterization theorems of Lawvere, Isbell and other authors.
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  9. Zofia Adamowicz (1992). A Sharp Version of the Bounded Matijasevich Conjecture and the End- Extension Problem. Journal of Symbolic Logic 57 (2):597-616.
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  10. Zofia Adamowicz (1991). On Maximal Theories. Journal of Symbolic Logic 56 (3):885-890.
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  11. Zofia Adamowicz (1977). On Finite Lattices of Degrees of Constructibility. Journal of Symbolic Logic 42 (3):349-371.
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  12. Zofia Adamowicz (1976). On Finite Lattices of Degrees of Constructibility of Reals. Journal of Symbolic Logic 41 (2):313-322.
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  13. Zofia Adamowicz (1976). One More Aspect of Forcing and Omitting Types. Journal of Symbolic Logic 41 (1):73-80.
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  14. Zofia Adamowicz & Teresa Bigorajska (2001). Existentially Closed Structures and Gödel's Second Incompleteness Theorem. Journal of Symbolic Logic 66 (1):349-356.
    We prove that any 1-closed (see def 1.1) model of the Π 2 consequences of PA satisfies ¬Cons PA which gives a proof of the second Godel incompleteness theorem without the use of the Godel diagonal lemma. We prove a few other theorems by the same method.
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  15. M. E. Adams, K. V. adaricheva, W. Dziobiak & A. V. Kravchenko (2004). Open Questions Related to the Problem of Birkhoff and Maltsev. Studia Logica 78 (1-2):357 - 378.
    The Birkhoff-Maltsev problem asks for a characterization of those lattices each of which is isomorphic to the lattice L(K) of all subquasivarieties for some quasivariety K of algebraic systems. The current status of this problem, which is still open, is discussed. Various unsolved questions that are related to the Birkhoff-Maltsev problem are also considered, including ones that stem from the theory of propositional logics.
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  16. M. E. Adams & W. Dziobiak (1995). Joins of Minimal Quasivarieties. Studia Logica 54 (3):371 - 389.
    LetL(K) denote the lattice (ordered by inclusion) of quasivarieties contained in a quasivarietyK and letD 2 denote the variety of distributive (0, 1)-lattices with 2 additional nullary operations. In the present paperL(D 2) is described. As a consequence, ifM+N stands for the lattice join of the quasivarietiesM andN, then minimal quasivarietiesV 0,V 1, andV 2 are given each of which is generated by a 2-element algebra and such that the latticeL(V 0+V1), though infinite, still admits an easy and nice description (...)
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  17. K. V. Adaricheva & V. A. Gorbunov (2004). On the Structure of Lattices of Subquasivarieties of Congruence-Noetherian Quasivarieties. Studia Logica 78 (1-2):35 - 44.
    We study the structure of algebraic -closed subsets of an algebraic lattice L, where is some Browerian binary relation on L, in the special case when the lattice of such subsets is an atomistic lattice. This gives an approach to investigate the atomistic lattices of congruence-Noetherian quasivarieties.
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  18. K. Adaricheva, R. Mckenzie, E. R. Zenk, M. Mar´ti & J. B. Nation (2006). The Jónsson-Kiefer Property. Studia Logica 83 (1-3):111 - 131.
    The least element 0 of a finite meet semi-distributive lattice is a meet of meet-prime elements. We investigate conditions under which the least element of an algebraic, meet semi-distributive lattice is a (complete) meet of meet-prime elements. For example, this is true if the lattice has only countably many compact elements, or if |L| < 2ℵ0, or if L is in the variety generated by a finite meet semi-distributive lattice. We give an example of an algebraic, meet semi-distributive lattice that (...)
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  19. Henry Africk (1974). Scott's Interpolation Theorem Fails for Lω1,Ω. Journal of Symbolic Logic 39 (1):124 - 126.
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  20. Tarek Sayed Ahmed (2008). On Complete Representations of Reducts of Polyadic Algebras. Studia Logica 89 (3):325 - 332.
    Following research initiated by Tarski, Craig and Németi, and futher pursued by Sain and others, we show that for certain subsets G of ω ω, atomic countable G polyadic algebras are completely representable. G polyadic algebras are obtained by restricting the similarity type and axiomatization of ω-dimensional polyadic algebras to finite quantifiers and substitutions in G. This contrasts the cases of cylindric and relation algebras.
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  21. Tarek Sayed Ahmed (2007). A Note on Neat Reducts. Studia Logica 85 (2):139 - 151.
    SC, CA, QA and QEA denote the class of Pinter’s substitution algebras, Tarski’s cylindric algebras, Halmos’ quasi-polyadic and quasi-polyadic equality algebras, respectively. Let . and . We show that the class of n dimensional neat reducts of algebras in K m is not elementary. This solves a problem in [2]. Also our result generalizes results proved in [1] and [2].
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  22. M. Aiguier & F. Barbier (2007). An Institution-Independent Proof of the Beth Definability Theorem. Studia Logica 85 (3):333 - 359.
    A few results generalizing well-known classical model theory ones have been obtained in institution theory these last two decades (e.g. Craig interpolation, ultraproduct, elementary diagrams). In this paper, we propose a generalized institution-independent version of the Beth definability theorem.
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  23. Seiki Akama (1987). Constructive Predicate Logic with Strong Negation and Model Theory. Notre Dame Journal of Formal Logic 29 (1):18-27.
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  24. Michael H. Albert (1987). A Preservation Theorem for EC-Structures with Applications. Journal of Symbolic Logic 52 (3):779-785.
    We characterize the model companions of universal Horn classes generated by a two-element algebra (or ordered two-element algebra). We begin by proving that given two mutually model consistent classes M and N of L (respectively L') structures, with $\mathscr{L} \subseteq \mathscr{L}'$ , M ec = N ec ∣ L , provided that an L-definability condition for the function and relation symbols of L' holds. We use this, together with Post's characterization of ISP(A), where A is a two-element algebra, to show (...)
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  25. Michael H. Albert & Rami P. Grossberg (1990). Rich Models. Journal of Symbolic Logic 55 (3):1292-1298.
    We define a rich model to be one which contains a proper elementary substructure isomorphic to itself. Existence, nonstructure, and categoricity theorems for rich models are proved. A theory T which has fewer than $\min(2^\lambda,\beth_2)$ rich models of cardinality $\lambda(\lambda > |T|)$ is totally transcendental. We show that a countable theory with a unique rich model in some uncountable cardinal is categorical in ℵ 1 and also has a unique countable rich model. We also consider a stronger notion of richness, (...)
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  26. Michael H. Albert & Ross Willard (1987). Injectives in Finitely Generated Universal Horn Classes. Journal of Symbolic Logic 52 (3):786-792.
    Let K be a finite set of finite structures. We give a syntactic characterization of the property: every element of K is injective in ISP(K). We use this result to establish that A is injective in ISP(A) for every two-element algebra A.
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  27. Natasha Alechina (1995). On a Decidable Generalized Quantifier Logic Corresponding to a Decidable Fragment of First-Order Logic. Journal of Logic, Language and Information 4 (3):177-189.
    Van Lambalgen (1990) proposed a translation from a language containing a generalized quantifierQ into a first-order language enriched with a family of predicatesR i, for every arityi (or an infinitary predicateR) which takesQxg(x, y1,..., yn) to x(R(x, y1,..., y1) (x,y1,...,yn)) (y 1,...,yn are precisely the free variables ofQx). The logic ofQ (without ordinary quantifiers) corresponds therefore to the fragment of first-order logic which contains only specially restricted quantification. We prove that it is decidable using the method of analytic tableaux. Related (...)
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  28. Gerard Allwein & J. Michael Dunn (1993). Kripke Models for Linear Logic. Journal of Symbolic Logic 58 (2):514-545.
    We present a Kripke model for Girard's Linear Logic (without exponentials) in a conservative fashion where the logical functors beyond the basic lattice operations may be added one by one without recourse to such things as negation. You can either have some logical functors or not as you choose. Commutatively and associatively are isolated in such a way that the base Kripke model is a model for noncommutative, nonassociative Linear Logic. We also extend the logic by adding a coimplication operator, (...)
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  29. Agostinho Almeida (2009). Canonical Extensions and Relational Representations of Lattices with Negation. Studia Logica 91 (2):171 - 199.
    This work is part of a wider investigation into lattice-structured algebras and associated dual representations obtained via the methodology of canonical extensions. To this end, here we study lattices, not necessarily distributive, with negation operations. We consider equational classes of lattices equipped with a negation operation ¬ which is dually self-adjoint (the pair (¬,¬) is a Galois connection) and other axioms are added so as to give classes of lattices in which the negation is De Morgan, orthonegation, antilogism, pseudocomplementation or (...)
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  30. Joseph S. Alper & Mark Bridger (1997). Mathematics, Models and Zeno's Paradoxes. Synthese 110 (1):143-166.
    A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that in (...)
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  31. Elias H. Alves (1984). Paraconsistent Logic and Model Theory. Studia Logica 43 (1-2):17 - 32.
    The object of this paper is to show how one is able to construct a paraconsistent theory of models that reflects much of the classical one. In other words the aim is to demonstrate that there is a very smooth and natural transition from the model theory of classical logic to that of certain categories of paraconsistent logic. To this end we take an extension of da Costa''sC 1 = (obtained by adding the axiom A A) and prove for it (...)
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  32. Klaus Ambos-Spies, Peter A. Fejer, Steffen Lempp & Manuel Lerman (1996). Decidability of the Two-Quantifier Theory of the Recursively Enumerable Weak Truth-Table Degrees and Other Distributive Upper Semi-Lattices. Journal of Symbolic Logic 61 (3):880-905.
    We give a decision procedure for the ∀∃-theory of the weak truth-table (wtt) degrees of the recursively enumerable sets. The key to this decision procedure is a characterization of the finite lattices which can be embedded into the r.e. wtt-degrees by a map which preserves the least and greatest elements: a finite lattice has such an embedding if and only if it is distributive and the ideal generated by its cappable elements and the filter generated by its cuppable elements are (...)
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  33. Anders Andersson (2002). On Second-Order Generalized Quantifiers and Finite Structures. Annals of Pure and Applied Logic 115 (1--3):1--32.
  34. H. Andréka & I. Németi (1985). On the Number of Generators of Cylindric Algebras. Journal of Symbolic Logic 50 (4):865-873.
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  35. H. Andréka, I. Németi & R. J. Thompson (1990). Weak Cylindric Set Algebras and Weak Subdirect Indecomposability. Journal of Symbolic Logic 55 (2):577-588.
    In this note we prove that the abstract property "weakly subdirectly indecomposable" does not characterize the class IWs α of weak cylindric set algebras. However, we give another (similar) abstract property characterizing IWs α . The original property does characterize the directed unions of members of $\mathrm{IWs}_alpha \operatorname{iff} \alpha$ is countable. Free algebras will be shown to satisfy the original property.
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  36. Hajnal Andréka, Steven Givant & István Németi (1994). The Lattice of Varieties of Representable Relation Algebras. Journal of Symbolic Logic 59 (2):631-661.
    We shall show that certain natural and interesting intervals in the lattice of varieties of representable relation algebras embed the lattice of all subsets of the natural numbers, and therefore must have a very complicated lattice-theoretic structure.
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  37. Peter B. Andrews (1972). General Models, Descriptions, and Choice in Type Theory. Journal of Symbolic Logic 37 (2):385-394.
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  38. Peter B. Andrews (1972). General Models and Extensionality. Journal of Symbolic Logic 37 (2):395-397.
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  39. Arthur W. Apter (1985). An AD-Like Model. Journal of Symbolic Logic 50 (2):531-543.
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  40. Andrew Arana (2005). Possible M-Diagrams of Models of Arithmetic. In Stephen Simpson (ed.), Reverse Mathematics 2001.
    In this paper I begin by extending two results of Solovay; the first characterizes the possible Turing degrees of models of True Arithmetic (TA), the complete first-order theory of the standard model of PA, while the second characterizes the possible Turing degrees of arbitrary completions of P. I extend these two results to characterize the possible Turing degrees of m-diagrams of models of TA and of arbitrary complete extensions of PA. I next give a construction showing that the conditions Solovay (...)
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  41. Andrew Arana (2001). Solovay's Theorem Cannot Be Simplified. Annals of Pure and Applied Logic 112 (1):27-41.
    In this paper we consider three potential simplifications to a result of Solovay’s concerning the Turing degrees of nonstandard models of arbitrary completions of first-order Peano Arithmetic (PA). Solovay characterized the degrees of nonstandard models of completions T of PA, showing that they are the degrees of sets X such that there is an enumeration R ≤T X of an “appropriate” Scott set and there is a family of functions (tn)n∈ω, ∆0 n(X) uniformly in n, such that lim tn(s) s→∞.
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  42. Ayda I. Arruda, Newton C. A. Costdaa & R. Chuaqui (eds.) (1977). Non-Classical Logics, Model Theory, and Computability: Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, Brazil, July 11-17, 1976. [REVIEW] Sale Distributors for the U.S.A. And Canada, Elsevier/North-Holland.
  43. Sergei Artemov & Giorgie Dzhaparidze (1990). Finite Kripke Models and Predicate Logics of Provability. Journal of Symbolic Logic 55 (3):1090-1098.
    The paper proves a predicate version of Solovay's well-known theorem on provability interpretations of modal logic: If a closed modal predicate-logical formula R is not valid in some finite Kripke model, then there exists an arithmetical interpretation f such that $PA \nvdash fR$ . This result implies the arithmetical completeness of arithmetically correct modal predicate logics with the finite model property (including the one-variable fragments of QGL and QS). The proof was obtained by adding "the predicate part" as a specific (...)
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  44. F. G. Asenjo (1967). Rings of Term-Relation Numbers as Non-Standard Models. Notre Dame Journal of Formal Logic 8 (1-2):24-26.
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  45. C. J. Ash (1994). On Countable Fractions From an Elementary Class. Journal of Symbolic Logic 59 (4):1410-1413.
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  46. David Asperó (2002). A Maximal Bounded Forcing Axiom. Journal of Symbolic Logic 67 (1):130-142.
    After presenting a general setting in which to look at forcing axioms, we give a hierarchy of generalized bounded forcing axioms that correspond level by level, in consistency strength, with the members of a natural hierarchy of large cardinals below a Mahlo. We give a general construction of models of generalized bounded forcing axioms. Then we consider the bounded forcing axiom for a class of partially ordered sets Γ 1 such that, letting Γ 0 be the class of all stationary-set-preserving (...)
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  47. David Asperó & Philip D. Welch (2002). Bounded Martin's Maximum, Weak [Image] Cardinals, and [Image]. Journal of Symbolic Logic 67 (3):1141 - 1152.
    We prove that a form of the $Erd\H{o}s$ property (consistent with $V = L\lbrack H_{\omega_2}\rbrack$ and strictly weaker than the Weak Chang's Conjecture at ω1), together with Bounded Martin's Maximum implies that Woodin's principle $\psi_{AC}$ holds, and therefore 2ℵ0 = ℵ2. We also prove that $\psi_{AC}$ implies that every function $f: \omega_1 \rightarrow \omega_1$ is bounded by some canonical function on a club and use this to produce a model of the Bounded Semiproper Forcing Axiom in which Bounded Martin's Maximum (...)
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  48. Jeremy Avigad & Richard Sommer (1999). The Model-Theoretic Ordinal Analysis of Theories of Predicative Strength. Journal of Symbolic Logic 64 (1):327-349.
    We use model-theoretic methods described in [3] to obtain ordinal analyses of a number of theories of first- and second-order arithmetic, whose proof-theoretic ordinals are less than or equal to Γ0.
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  49. Jeremy Avigad & Richard Sommer (1997). A Model-Theoretic Approach to Ordinal Analysis. Bulletin of Symbolic Logic 3 (1):17-52.
    We describe a model-theoretic approach to ordinal analysis via the finite combinatorial notion of an α-large set of natural numbers. In contrast to syntactic approaches that use cut elimination, this approach involves constructing finite sets of numbers with combinatorial properties that, in nonstandard instances, give rise to models of the theory being analyzed. This method is applied to obtain ordinal analyses of a number of interesting subsystems of first- and second-order arithmetic.
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  50. Uri Avraham & Saharon Shelah (1982). Forcing with Stable Posets. Journal of Symbolic Logic 47 (1):37-42.
    The class of stable posets is defined and investigated. We give a forcing construction of a universe of set theory which satisfies a weak form of Martin's Axiom and $2^{\aleph_0} > \aleph_1$ and yet some propositions which follow from CH hold in this universe.
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