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

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  1.  7
    Jon Barwise (1975). Admissible Sets and Structures: An Approach to Definability Theory. Springer-Verlag.
  2.  9
    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.
    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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  3. Gerhard Jäger (1986). Theories for Admissible Sets: A Unifying Approach to Proof Theory. Bibliopolis.
     
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  4.  22
    Jacob Lurie (1999). Anti-Admissible Sets. Journal of Symbolic Logic 64 (2):407-435.
    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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  5.  12
    Barbara Majcher‐Iwanow (2008). Polish Group Actions, Nice Topologies, and Admissible Sets. Mathematical Logic Quarterly 54 (6):597-616.
    Let G be a closed subgroup of S∞ and X be a Polish G -space. To every x ∈ X we associate an admissible set Ax and show how questions about X which involve Baire category can be formalized in Ax.
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  6.  31
    Jon Barwise (1969). Infinitary Logic and Admissible Sets. Journal of Symbolic Logic 34 (2):226-252.
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  7.  2
    Mark Nadel (1974). Scott Sentences and Admissible Sets. Annals of Mathematical Logic 7 (2-3):267-294.
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  8.  36
    H. Jerome Keisler & Julia F. Knight (2004). Barwise: Infinitary Logic and Admissible Sets. Bulletin of Symbolic Logic 10 (1):4-36.
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  9.  12
    Alan Adamson (1978). Admissible Sets and the Saturation of Structures. Annals of Mathematical Logic 14 (2):111-157.
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  10. John S. Schlipf (1977). A Guide to the Identification of Admissible Sets Above Structures. Annals of Mathematical Logic 12 (2):151-192.
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  11.  5
    Judy Green (1974). Σ1 Compactness for Next Admissible Sets. Journal of Symbolic Logic 39 (1):105 - 116.
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  12.  6
    Menachem Magidor, Saharon Shelah & Jonathan Stavi (1984). Countably Decomposable Admissible Sets. Annals of Pure and Applied Logic 26 (3):287-361.
    The known results about Σ 1 -completeness, Σ 1 -compactness, ordinal omitting etc. are given a unified treatment, which yields many new examples. It is shown that the unifying theorem is best possible in several ways, assuming V = L.
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  13. Nigel Cutland (1973). Model Theory on Admissible Sets. Annals of Mathematical Logic 5 (4):257-289.
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  14.  2
    E. G. K. Lopez-Escobar (1971). Review: Jon Barwise, Infinitary Logic and Admissible Sets. [REVIEW] Journal of Symbolic Logic 36 (1):156-157.
  15.  4
    Bernd I. Dahn (1978). Admissible Sets and Structures. Studia Logica 37 (3):297-299.
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  16.  1
    Judy Green (1977). Next $P$ Admissible Sets Are of Cofinality $\Omega$. Notre Dame Journal of Formal Logic 18 (1):175-176.
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  17. Carl E. Bredlau (1979). Admissible Sets and Recursive Equivalence Types. Notre Dame Journal of Formal Logic 20 (2):355-365.
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  18. Judy Green (1974). $Sigma_1$ Compactness for Next Admissible Sets. Journal of Symbolic Logic 39 (1):105-116.
  19. Judy Green (1975). A Note on ${\Cal P}$-Admissible Sets with Urelements. Notre Dame Journal of Formal Logic 16 (3):415-417.
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  20. E. G. K. Lopez-Escobar (1971). Barwise Jon. Infinitary Logic and Admissible Sets. Journal of Symbolic Logic 36 (1):156-157.
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  21. Mark Nadel (1978). Barwise Jon. Admissible Sets and Structures. An Approach to Definability Theory. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, Heidelberg, and New York, 1975, XIV + 394 Pp. [REVIEW] Journal of Symbolic Logic 43 (1):139-144.
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  22. Mark Nadel (1978). Review: Jon Barwise, Admissible Sets and Structures. An Approach to Definability Theory. [REVIEW] Journal of Symbolic Logic 43 (1):139-144.
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  23.  20
    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.
    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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  24.  1
    Wolfgang Maass (1978). Inadmissibility, Tame R.E. Sets and the Admissible Collapse. Annals of Mathematical Logic 13 (2):149-170.
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  25. Michael Machtey (1971). Admissible Ordinals and Lattices of Α-R.E. Sets. Annals of Mathematical Logic 2 (4):379-417.
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  26. 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.
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  27. 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.
     
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  28. Steven Homer (1981). Maass Wolfgang. Inadmissibility, Tame R.E. Sets and the Admissible Collapse. Annals of Mathematical Logic, Vol. 13 No. 2 , Pp. 149–170. [REVIEW] Journal of Symbolic Logic 46 (3):665-667.
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  29. Richard A. Platek (1969). Sacks Gerald E.. Metarecursively Enumerable Sets and Admissible Ordinals. Bulletin of the American Mathematical Society, Vol. 72 , Pp. 59–64.Sacks Gerald E.. Post's Problem, Admissible Ordinals, and Regularity. Transactions of the American Mathematical Society, Vol. 124 , Pp. 1–23.Sacks Gerald E.. Metarecursion Theory. Sets, Models and Recursion Theory, Proceedings of the Summer School in Mathematical Logic and Tenth Logic Colloquium, Leicester, August-September 1965, Edited by Crossley John N., Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam, and Humanities Press, New York, 1967, Pp. 243–263.Driscoll Graham C. Jr., Metarecursively Enumerable Sets and Their Metadegrees. [REVIEW] Journal of Symbolic Logic 34 (1):115-116.
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  30. Michael Glanzberg (2004). A Contextual-Hierarchical Approach to Truth and the Liar Paradox. Journal of Philosophical Logic 33 (1):27-88.
    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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  31. Heikki Heikkilä & Jouko Väänänen (1994). Reflection of Long Game Formulas. Mathematical Logic Quarterly 40 (3):381-392.
    We study game formulas the truth of which is determined by a semantical game of uncountable length. The main theme is the study of principles stating reflection of these formulas in various admissible sets. This investigation leads to two weak forms of strict-II11 reflection . We show that admissible sets such as H and Lω2 which fail to have strict-II11 reflection, may or may not, depending on set-theoretic hypotheses satisfy one or both of these weaker forms.
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  32. Barbara Majcher-Iwanow (2012). Polish Group Actions and Effectivity. Archive for Mathematical Logic 51 (5-6):563-573.
    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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  33.  4
    Michael Rathjen (1993). How to Develop Proof‐Theoretic Ordinal Functions on the Basis of Admissible Ordinals. Mathematical Logic Quarterly 39 (1):47-54.
    In ordinal analysis of impredicative theories so-called collapsing functions are of central importance. Unfortunately, the definition procedure of these functions makes essential use of uncountable cardinals whereas the notation system that they call into being corresponds to a recursive ordinal. It has long been claimed that, instead, one should manage to develop such functions directly on the basis of admissible ordinals. This paper is meant to show how this can be done. Interpreting the collapsing functions as operating directly on (...)
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  34.  35
    Robert Goldblatt & Michael Kane (2010). An Admissible Semantics for Propositionally Quantified Relevant Logics. Journal of Philosophical Logic 39 (1):73 - 100.
    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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  35.  7
    Sy D. Friedman (1979). HC of an Admissible Set. Journal of Symbolic Logic 44 (1):95-102.
    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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  36. Angelika Kratzer (2005). Constraining Premise Sets for Counterfactuals. Journal of Semantics 22 (2):153-158.
    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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  37.  4
    Jeroen P. Goudsmit & Rosalie Iemhoff (2014). On Unification and Admissible Rules in Gabbay–de Jongh Logics. Annals of Pure and Applied Logic 165 (2):652-672.
    In this paper we study the admissible rules of intermediate logics. We establish some general results on extensions of models and sets of formulas. These general results are then employed to provide a basis for the admissible rules of the Gabbay–de Jongh logics and to show that these logics have finitary unification type.
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  38.  6
    Matthias Schröder (2007). Admissible Representations for Probability Measures. Mathematical Logic Quarterly 53 (4):431-445.
    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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  39.  15
    Theodore A. Slaman (1986). On the Kleene Degrees of Π11 Sets. Journal of Symbolic Logic 51 (2):352 - 359.
    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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  40.  1
    M. Schroder (2002). Effectivity in Spaces with Admissible Multirepresentations. Mathematical Logic Quarterly 48 (S1):78-90.
    The property of admissibility of representations plays an important role in Type–2 Theory of Effectivity . TTE defines computability on sets with continuum cardinality via representations. Admissibility is known to be indispensable for guaranteeing reasonable effectivity properties of the used representations.The question arises whether every function that is computable with respect to arbritrary representations is also computable with respect to closely related admissible ones. We define three operators which transform representations into admissible ones in such a way (...)
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  41.  11
    Boniface Mbih (1995). On Admissible Strategies and Manipulation of Social Choice Procedures. Theory and Decision 39 (2):169-188.
    A collective choice mechanism can be viewed as a game in normal form; in this article it is shown, for very attractive rules and for sets with any number of alternatives, how individuals involved in a collective decision problem can construct the preferences they choose to express. An example is given with a version of plurality rule. Manipulability results are deduced from such a characterization.
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  42.  26
    Noam Greenberg (2005). The Role of True Finiteness in the Admissible Recursively Enumerable Degrees. Bulletin of Symbolic Logic 11 (3):398-410.
    We show, however, that this is not always the case.
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  43.  6
    Sergei Odintsov & Vladimir Rybakov (2013). Unification and Admissible Rules for Paraconsistent Minimal Johanssonsʼ Logic J and Positive Intuitionistic Logic. Annals of Pure and Applied Logic 164 (7-8):771-784.
    We study unification problem and problem of admissibility for inference rules in minimal Johanssonsʼ logic J and positive intuitionistic logic IPC+. This paper proves that the problem of admissibility for inference rules with coefficients is decidable for the paraconsistent minimal Johanssonsʼ logic J and the positive intuitionistic logic IPC+. Using obtained technique we show also that the unification problem for these logics is also decidable: we offer algorithms which compute complete sets of unifiers for any unifiable formula. Checking just (...)
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  44.  6
    Shaughan Lavine (1993). Generalized Reduction Theorems for Model-Theoretic Analogs of the Class of Coanalytic Sets. Journal of Symbolic Logic 58 (1):81-98.
    Let A be an admissible set. A sentence of the form ∀R̄φ is a ∀1(A) (∀s 1(A),∀1(Lω1ω)) sentence if φ ∈ A (φ is $\bigvee\Phi$ , where Φ is an A-r.e. set of sentences from A; φ ∈ Lω1ω). A sentence of the form ∃R̄φ is an ∃2(A) (∃s 2(A),∃2(Lω1ω)) sentence if φ is a ∀1(A) (∀s 1(A),∀1(Lω1ω)) sentence. A class of structures is, for example, a ∀1(A) class if it is the class of models of a ∀1(A) sentence. (...)
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  45.  2
    Mark Nadel & Jonathan Stavi (1977). The Pure Part of HYP(M). Journal of Symbolic Logic 42 (1):33-46.
    Let M be a structure for a language L on a set M of urelements. HYP(M) is the least admissible set above M. In § 1 we show that pp(HYP(M)) [ = the collection of pure sets in HYP(M] is determined in a simple way by the ordinal α = ⚬(HYP(M)) and the $\mathscr{L}_{\propto\omega}$ theory of M up to quantifier rank α. In § 2 we consider the question of which pure countable admissible sets are of (...)
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  46.  2
    Jens Erik Fenstad, R. O. Gandy & Gerald E. Sacks (eds.) (1978). Generalized Recursion Theory Ii: Proceedings of the 1977 Oslo Symposium. Sole Distributors for the U.S.A. And Canada, Elsevier North-Holland.
    GENERALIZED RECUBION THEORY II © North-Holland Publishing Company (1978) MONOTONE QUANTIFIERS AND ADMISSIBLE SETS Ion Barwise University of Wisconsin ...
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  47. Mark Nadel & Jonathan Stavi (1977). The Pure Part of $Mathrm{HYP}(Mathscr{M}$). Journal of Symbolic Logic 42 (1):33-46.
    Let $\mathscr{M}$ be a structure for a language $\mathscr{L}$ on a set $M$ of urelements. $\mathrm{HYP}(\mathscr{M})$ is the least admissible set above $\mathscr{M}$. In $\S 1$ we show that $pp(\mathrm{HYP}(\mathscr{M})) \lbrack = \text{the collection of pure sets in} \mathrm{HYP}(\mathscr{M}\rbrack$ is determined in a simple way by the ordinal $\alpha = \circ(\mathrm{HYP}(\mathscr{M}))$ and the $\mathscr{L}_{\propto\omega}$ theory of $\mathscr{M}$ up to quantifier rank $\alpha$. In $\S 2$ we consider the question of which pure countable admissible sets are of (...)
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  48. Emil Jeřábek (2007). Complexity of Admissible Rules. Archive for Mathematical Logic 46 (2):73-92.
    We investigate the computational complexity of deciding whether a given inference rule is admissible for some modal and superintuitionistic logics. We state a broad condition under which the admissibility problem is coNEXP-hard. We also show that admissibility in several well-known systems (including GL, S4, and IPC) is in coNE, thus obtaining a sharp complexity estimate for admissibility in these systems.
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  49.  45
    Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane (2010). Coherent Choice Functions Under Uncertainty. Synthese 172 (1):157 - 176.
    We discuss several features of coherent choice functions —where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the (...)
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  50. Shaughan Lavine (1992). A Spector-Gandy Theorem for cPCd(A) Classes. Journal of Symbolic Logic 57 (2):478 - 500.
    Let U be an admissible structure. A cPCd(U) class is the class of all models of a sentence of the form $\neg\exists\bar{K} \bigwedge \Phi$ , where K̄ is an U-r.e. set of relation symbols and φ is an U-r.e. set of formulas of L∞ω that are in U. The main theorem is a generalization of the following: Let U be a pure countable resolvable admissible structure such that U is not Σ-elementarily embedded in HYP(U). Then a class K (...)
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