Search results for 'Admissible sets' (try it on Scholar)

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  1. Diego Rojas-Rebolledo (2012). Bounds on the Strength of Ordinal Definable Determinacy in Small Admissible Sets. Notre Dame Journal of Formal Logic 53 (3):351-371.score: 82.0
    We give upper and lower bounds for the strength of ordinal definable determinacy in a small admissible set. The upper bound is roughly a premouse with a measurable cardinal $\kappa$ of Mitchell order $\kappa^{++}$ and $\omega$ successors. The lower bound are models of ZFC with sequences of measurable cardinals, extending the work of Lewis, below a regular limit of measurable cardinals.
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  2. Jon Barwise (1975). Admissible Sets and Structures: An Approach to Definability Theory. Springer-Verlag.score: 75.0
  3. Gerhard Jäger (1986). Theories for Admissible Sets: A Unifying Approach to Proof Theory. Bibliopolis.score: 75.0
     
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  4. Dieter Probst (2005). On the Relationship Between Fixed Points and Iteration in Admissible Set Theory Without Foundation. Archive for Mathematical Logic 44 (5):561-580.score: 66.0
    In this article we show how to use the result in Jäger and Probst [7] to adapt the technique of pseudo-hierarchies and its use in Avigad [1] to subsystems of set theory without foundation. We prove that the theory KPi0 of admissible sets without foundation, extended by the principle (Σ-FP), asserting the existence of fixed points of monotone Σ operators, has the same proof-theoretic ordinal as KPi0 extended by the principle (Σ-TR), that allows to iterate Σ operations along (...)
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  5. Jacob Lurie (1999). Anti-Admissible Sets. Journal of Symbolic Logic 64 (2):407-435.score: 60.0
    Aczel's theory of hypersets provides an interesting alternative to the standard view of sets as inductively constructed, well-founded objects, thus providing a convienent formalism in which to consider non-well-founded versions of classically well-founded constructions, such as the "circular logic" of [3]. This theory and ZFC are mutually interpretable; in particular, any model of ZFC has a canonical "extension" to a non-well-founded universe. The construction of this model does not immediately generalize to weaker set theories such as the theory of (...)
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  6. Barbara Majcher‐Iwanow (2008). Polish Group Actions, Nice Topologies, and Admissible Sets. Mathematical Logic Quarterly 54 (6):597-616.score: 59.0
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  7. Michael Glanzberg (2004). A Contextual-Hierarchical Approach to Truth and the Liar Paradox. Journal of Philosophical Logic 33 (1):27-88.score: 45.0
    This paper presents an approach to truth and the Liar paradox which combines elements of context dependence and hierarchy. This approach is developed formally, using the techniques of model theory in admissible sets. Special attention is paid to showing how starting with some ideas about context drawn from linguistics and philosophy of language, we can see the Liar sentence to be context dependent. Once this context dependence is properly understood, it is argued, a hierarchical structure emerges which is (...)
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  8. Jon Barwise (1969). Infinitary Logic and Admissible Sets. Journal of Symbolic Logic 34 (2):226-252.score: 45.0
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  9. H. Jerome Keisler & Julia F. Knight (2004). Barwise: Infinitary Logic and Admissible Sets. Bulletin of Symbolic Logic 10 (1):4-36.score: 45.0
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  10. Alan Adamson (1978). Admissible Sets and the Saturation of Structures. Annals of Mathematical Logic 14 (2):111-157.score: 45.0
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  11. Bernd I. Dahn (1978). Admissible Sets and Structures. Studia Logica 37 (3):297-299.score: 45.0
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  12. Carl E. Bredlau (1979). Admissible Sets and Recursive Equivalence Types. Notre Dame Journal of Formal Logic 20 (2):355-365.score: 45.0
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  13. Nigel Cutland (1973). Model Theory on Admissible Sets. Annals of Mathematical Logic 5 (4):257-289.score: 45.0
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  14. Judy Green (1974). Σ1 Compactness for Next Admissible Sets. Journal of Symbolic Logic 39 (1):105 - 116.score: 45.0
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  15. Judy Green (1974). $Sigma_1$ Compactness for Next Admissible Sets. Journal of Symbolic Logic 39 (1):105-116.score: 45.0
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  16. Judy Green (1975). A Note on ${\Cal P}$-Admissible Sets with Urelements. Notre Dame Journal of Formal Logic 16 (3):415-417.score: 45.0
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  17. Judy Green (1977). Next $P$ Admissible Sets Are of Cofinality $\Omega$. Notre Dame Journal of Formal Logic 18 (1):175-176.score: 45.0
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  18. E. G. K. Lopez-Escobar (1971). Review: Jon Barwise, Infinitary Logic and Admissible Sets. [REVIEW] Journal of Symbolic Logic 36 (1):156-157.score: 45.0
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  19. Menachem Magidor, Saharon Shelah & Jonathan Stavi (1984). Countably Decomposable Admissible Sets. Annals of Pure and Applied Logic 26 (3):287-361.score: 45.0
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  20. Barbara Majcher-Iwanow (2012). Polish Group Actions and Effectivity. Archive for Mathematical Logic 51 (5-6):563-573.score: 45.0
    We extend a theorem of Barwise and Nadel describing the relationship between approximations of canonical Scott sentences and admissible sets to the case of orbit equivalence relations induced on an arbitrary Polish space by a Polish group action.
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  21. Mark Nadel (1978). Review: Jon Barwise, Admissible Sets and Structures. An Approach to Definability Theory. [REVIEW] Journal of Symbolic Logic 43 (1):139-144.score: 45.0
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  22. Mark Nadel (1974). Scott Sentences and Admissible Sets. Annals of Mathematical Logic 7 (2-3):267-294.score: 45.0
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  23. John S. Schlipf (1977). A Guide to the Identification of Admissible Sets Above Structures. Annals of Mathematical Logic 12 (2):151-192.score: 45.0
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  24. Steven Homer (1981). Review: Wolfgang Maass, Inadmissibility, Tame R.E. Sets and the Admissible Collapse; Wolfgang Maass, On $Alpha$- and $Beta$-Recursively Enumerable Degrees. [REVIEW] Journal of Symbolic Logic 46 (3):665-667.score: 36.0
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  25. Sy D. Friedman (1979). HC of an Admissible Set. Journal of Symbolic Logic 44 (1):95-102.score: 36.0
    If A is an admissible set, let HC(A) = {x∣ x ∈ A and x is hereditarily countable in A}. Then HC(A) is admissible. Corollaries are drawn characterizing the "real parts" of admissible sets and the analytical consequences of admissible set theory.
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  26. Wolfgang Maass (1978). Inadmissibility, Tame R.E. Sets and the Admissible Collapse. Annals of Mathematical Logic 13 (2):149-170.score: 36.0
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  27. Michael Machtey (1971). Admissible Ordinals and Lattices of Α-R.E. Sets. Annals of Mathematical Logic 2 (4):379-417.score: 36.0
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  28. M. Makkai (1977). An “Admissible” Generalization of a Theorem on Countable ∑11 Sets of Reals with Applications. Annals of Mathematical Logic 11 (1):1-30.score: 36.0
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  29. Jeremy Avigad (2002). An Ordinal Analysis of Admissible Set Theory Using Recursion on Ordinal Notations. Journal of Mathematical Logic 2 (01):91-112.score: 34.0
    The notion of a function from ℕ to ℕ defined by recursion on ordinal notations is fundamental in proof theory. Here this notion is generalized to functions on the universe of sets, using notations for well orderings longer than the class of ordinals. The generalization is used to bound the rate of growth of any function on the universe of sets that is Σ1-definable in Kripke–Platek admissible set theory with an axiom of infinity. Formalizing the argument provides (...)
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  30. Heikki Heikkilä & Jouko Väänänen (1994). Reflection of Long Game Formulas. Mathematical Logic Quarterly 40 (3):381-392.score: 30.0
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  31. Gerhard Jäger & Thomas Strahm (2001). Upper Bounds for Metapredicative Mahlo in Explicit Mathematics and Admissible Set Theory. Journal of Symbolic Logic 66 (2):935-958.score: 28.0
    In this article we introduce systems for metapredicative Mahlo in explicit mathematics and admissible set theory. The exact upper proof-theoretic bounds of these systems are established.
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  32. Robert Goldblatt & Michael Kane (2010). An Admissible Semantics for Propositionally Quantified Relevant Logics. Journal of Philosophical Logic 39 (1):73 - 100.score: 27.0
    The Routley-Meyer relational semantics for relevant logics is extended to give a sound and complete model theory for many propositionally quantified relevant logics (and some non-relevant ones). This involves a restriction on which sets of worlds are admissible as propositions, and an interpretation of propositional quantification that makes ∀ pA true when there is some true admissible proposition that entails all p -instantiations of A . It is also shown that without the admissibility qualification many of the (...)
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  33. Matthias Schröder (2007). Admissible Representations for Probability Measures. Mathematical Logic Quarterly 53 (4):431-445.score: 23.0
    In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of type-2 theory of effectivity. This gives rise to a natural representation of the set of Borel probability measures on X. We compare this representation to a canonically constructed representation which encodes a Borel probability measure as a lower semicontinuous function from the open sets to the unit interval. We show that this canonical (...)
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  34. Angelika Kratzer (2005). Constraining Premise Sets for Counterfactuals. Journal of Semantics 22 (2):153-158.score: 21.0
    This note is a reply to ‘On the Lumping Semantics of Counterfactuals’ by Makoto Kanazawa, Stefan Kaufmann and Stanley Peters. It shows first that the first triviality result obtained by Kanazawa, Kaufmann, and Peters is already ruled out by the constraints on admissible premise sets listed in Kratzer (1989). Second, and more importantly, it points out that the results obtained by Kanazawa, Kaufmann, and Peters are obsolete in view of the revised analysis of counterfactuals in Kratzer (1990, 2002).
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  35. Fabio G. Cozman (2012). Sets of Probability Distributions, Independence, and Convexity. Synthese 186 (2):577-600.score: 21.0
    This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli’s discussion of “convex Bayesianism” (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of “strong independence” (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli’s results and (...)
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  36. K. J. Barwise, R. O. Gandy & Y. N. Moschovakis (1971). The Next Admissible Set. Journal of Symbolic Logic 36 (1):108-120.score: 21.0
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  37. Theodore A. Slaman (1986). On the Kleene Degrees of Π11 Sets. Journal of Symbolic Logic 51 (2):352 - 359.score: 21.0
    Let A and B be subsets of the reals. Say that A κ ≥ B, if there is a real a such that the relation "x ∈ B" is uniformly Δ 1 (a, A) in L[ ω x,a,A 1 , x,a,A]. This reducibility induces an equivalence relation $\equiv_\kappa$ on the sets of reals; the $\equiv_\kappa$ -equivalence class of a set is called its Kleene degree. Let K be the structure that consists of the Kleene degrees and the induced partial (...)
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  38. Alexander Citkin (2012). A Note on Admissible Rules and the Disjunction Property in Intermediate Logics. Archive for Mathematical Logic 51 (1-2):1-14.score: 21.0
    With any structural inference rule A/B, we associate the rule ${(A \lor p)/(B \lor p)}$ , providing that formulas A and B do not contain the variable p. We call the latter rule a join-extension ( ${\lor}$ -extension, for short) of the former. Obviously, for any intermediate logic with disjunction property, a ${\lor}$ -extension of any admissible rule is also admissible in this logic. We investigate intermediate logics, in which the ${\lor}$ -extension of each admissible rule is (...)
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  39. Christopher Menzel (2012). Sets and Worlds Again. Analysis 72 (2):304-309.score: 18.0
    Bringsjord (1985) argues that the definition W of possible worlds as maximal possible sets of propositions is incoherent. Menzel (1986a) notes that Bringsjord’s argument depends on the Powerset axiom and that the axiom can be reasonably denied. Grim (1986) counters that W can be proved to be incoherent without Powerset. Grim was right. However, the argument he provided is deeply flawed. The purpose of this note is to detail the problems with Grim’s argument and to present a sound alternative (...)
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  40. Alexej P. Pynko (2009). Distributive-Lattice Semantics of Sequent Calculi with Structural Rules. Logica Universalis 3 (1):59-94.score: 18.0
    The goal of the paper is to develop a universal semantic approach to derivable rules of propositional multiple-conclusion sequent calculi with structural rules, which explicitly involve not only atomic formulas, treated as metavariables for formulas, but also formula set variables (viz., metavariables for finite sets of formulas), upon the basis of the conception of model introduced in (Fuzzy Sets Syst 121(3):27–37, 2001). One of the main results of the paper is that any regular sequent calculus with structural rules (...)
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  41. Étienne Matheron & Miroslav Zelený (2007). Descriptive Set Theory of Families of Small Sets. Bulletin of Symbolic Logic 13 (4):482-537.score: 18.0
    This is a survey paper on the descriptive set theory of hereditary families of closed sets in Polish spaces. Most of the paper is devoted to ideals and σ-ideals of closed or compact sets.
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  42. Nikk Effingham (2012). Impure Sets May Be Located: A Reply to Cook. Thought 1 (4):330-336.score: 18.0
    Cook argues that impure sets are not located. But ‘location’ is an ambiguous word and when we resolve those ambiguities it turns out that on no resolution is Cook's argument compelling.
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  43. Siegfried Gottwald (2006). Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part I: Model-Based and Axiomatic Approaches. [REVIEW] Studia Logica 82 (2):211 - 244.score: 18.0
    For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets. We discuss here the corresponding situation for fuzzy set theory.Our emphasis will be on various approaches toward (more or less naively formed)universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets.
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  44. Paweł Kawa & Janusz Pawlikowski (2010). Extending Baire Property by Uncountably Many Sets. Journal of Symbolic Logic 75 (3):896-904.score: 18.0
    We show that for an uncountable κ in a suitable Cohen real model for any family {A ν } ν<κ of sets of reals there is a σ-homomorphism h from the σ-algebra generated by Borel sets and the sets A ν into the algebra of Baire subsets of 2 κ modulo meager sets such that for all Borel B, B is meager iff h(B) = 0. The proof is uniform, works also for random reals and the (...)
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  45. Wim Hordijk, Mike Steel & Stuart Kauffman (2012). The Structure of Autocatalytic Sets: Evolvability, Enablement, and Emergence. Acta Biotheoretica 60 (4):379-392.score: 18.0
    This paper presents new results from a detailed study of the structure of autocatalytic sets. We show how autocatalytic sets can be decomposed into smaller autocatalytic subsets, and how these subsets can be identified and classified. We then argue how this has important consequences for the evolvability, enablement, and emergence of autocatalytic sets. We end with some speculation on how all this might lead to a generalized theory of autocatalytic sets, which could possibly be applied to (...)
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  46. Serikzhan A. Badaev & Steffen Lempp (2009). A Decomposition of the Rogers Semilattice of a Family of D.C.E. Sets. Journal of Symbolic Logic 74 (2):618-640.score: 18.0
    Khutoretskii's Theorem states that the Rogers semilattice of any family of c.e. sets has either at most one or infinitely many elements. A lemma in the inductive step of the proof shows that no Rogers semilattice can be partitioned into a principal ideal and a principal filter. We show that such a partitioning is possible for some family of d.c.e. sets. In fact, we construct a family of c.e. sets which, when viewed as a family of d.c.e. (...)
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  47. Leigh M. Valen (1988). Species, Sets, and the Derivative Nature of Philosophy. Biology and Philosophy 3 (1):49-66.score: 18.0
    Concepts and methods originating in one discipline can distort the structure of another when they are applied to the latter. I exemplify this mostly with reference to systematic biology, especially problems which have arisen in relation to the nature of species. Thus the received views of classes, individuals (which term I suggest be replaced by units to avoid misunderstandings), and sets are all inapplicable, but each can be suitably modified. The concept of fuzzy set was developed to deal with (...)
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  48. Martin Kummer & Marcus Schaefer (2007). Cuppability of Simple and Hypersimple Sets. Notre Dame Journal of Formal Logic 48 (3):349-369.score: 18.0
    An incomplete degree is cuppable if it can be joined by an incomplete degree to a complete degree. For sets fulfilling some type of simplicity property one can now ask whether these sets are cuppable with respect to a certain type of reducibilities. Several such results are known. In this paper we settle all the remaining cases for the standard notions of simplicity and all the main strong reducibilities.
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  49. M. Carmen Sánchez (1998). Rational Choice on Non-Finite Sets by Means of Expansion-Contraction Axioms. Theory and Decision 45 (1):1-17.score: 18.0
    The rationalization of a choice function, in terms of assumptions that involve expansion or contraction properties of the feasible set, over non-finite sets is analyzed. Schwartz's results (1976), stated in the finite case, are extended to this more general framework. Moreover, a characterization result when continuity conditions are imposed on the choice function, as well as on the binary relation that rationalizes it, is presented.
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  50. L. Š Grinblat (2007). On Sets Not Belonging to Algebras. Journal of Symbolic Logic 72 (2):483-500.score: 18.0
    Let A₁,..., An, An+1 be a finite sequence of algebras of sets given on a set X, $\cup _{k=1}^{n}{\cal A}_{k}\neq \germ{P}(X)$, with more than $\frac{4}{3}n$ pairwise disjoint sets not belonging to An+1. It was shown in [4] and [5] that in this case $\cup _{k=1}^{n+1}{\cal A}_{k}\neq \germ{P}(X)$. Let us consider, instead An+1, a finite sequence of algebras An+1,..., An+l. It turns out that if for each natural i ≤ l there exist no less than $\frac{4}{3}(n+l)-\frac{l}{24}$ pairwise disjoint (...) not belonging to An+i, then $\cup _{k=1}^{n+1}{\cal A}_{k}\neq \germ{P}(X)$. But if l ≥ 195 and if for each natural i ≤ l there exist no less than $\frac{4}{3}(n+l)-\frac{l}{15}$ pairwise disjoint sets not belonging to An+i, then $\cup _{k=1}^{n+1}{\cal A}_{k}\neq \germ{P}(X)$. After consideration of finite sequences of algebras, it is natural to consider countable sequences of algebras. We obtained two essentially important theorems on a countable sequence of almost σ-algebras (the concept of almost σ-algebra was introduced in [4]). (shrink)
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