David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 58 (1):81-98 (1993)
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. Thus ∀1(A) is a class of classes of structures, and so forth. Let Mi be the structure $\langle i, 0$. Let Γ be a class of classes of structures. We say that a sequence $J_1,\ldots,J_i,\ldots, i < \omega$, of classes of structures is a Γ sequence if $J_i \in \Gamma, i < \omega$, and there is I ∈ Γ such that M ∈ Ji if and only if [M, Mi] ∈ I, where [,] is the disjoint sum. A class Γ of classes of structures has the easy uniformization property if for every Γ sequence $J_1,\ldots,J_i, \ldots, i < \omega$, there is a Γ sequence $J'_1,\ldots,J'_i,\ldots, i < \omega$, such that $J'_i \subseteq J_i, i < \omega, \bigcup J'_i = \bigcup J_i$, and the J'i are pairwise disjoint. The easy uniformization property is an effective version of Kuratowski's generalized reduction property that is closely related to Moschovakis's (topological) easy uniformization property. We show over countable structures that ∀1(A) and ∃2(A) have the easy uniformization property if A is a countable admissible set with an infinite member, that ∀s 1(Lα) and ∃s 2(Lα) have the easy uniformization property if α is countable, admissible, and not weakly stable, and that ∀1(Lω1ω) and ∃2(Lω1ω) have the easy uniformization property. The results proved are more general. The result for ∀s 1(Lα) answers a question of Vaught (1980)
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Carl G. Jockusch Jr & Tamara J. Lakins (2002). Generalized R-Cohesiveness and the Arithmetical Hierarchy: A Correction to "Generalized Cohesiveness". Journal of Symbolic Logic 67 (3):1078 - 1082.
P. Schlenker (2007). The Elimination of Self-Reference: Generalized Yablo-Series and the Theory of Truth. [REVIEW] Journal of Philosophical Logic 36 (3):251 - 307.
Saharon Shelah & Jouko Väänänen (2000). Stationary Sets and Infinitary Logic. Journal of Symbolic Logic 65 (3):1311-1320.
Matatyahu Rubin & Saharon Shelah (1983). On the Expressibility Hierarchy of Magidor-Malitz Quantifiers. Journal of Symbolic Logic 48 (3):542-557.
P. X. Monaghan (2010). A Novel Interpretation of Plato's Theory of Forms. Metaphysica 11 (1):63-78.
Kevin C. Klement, Russell's Paradox. Internet Encyclopedia of Philosophy.
Tom Linton (1991). Countable Structures, Ehrenfeucht Strategies, and Wadge Reductions. Journal of Symbolic Logic 56 (4):1325-1348.
Harvey Friedman & Lee Stanley (1989). A Borel Reducibility Theory for Classes of Countable Structures. Journal of Symbolic Logic 54 (3):894-914.
Shaughan Lavine (1992). A Spector-Gandy Theorem for cPCd(A) Classes. Journal of Symbolic Logic 57 (2):478 - 500.
Shaughan Lavine (1991). Dual Easy Uniformization and Model-Theoretic Descriptive Set Theory. Journal of Symbolic Logic 56 (4):1290-1316.
Added to index2009-01-28
Total downloads4 ( #299,063 of 1,692,585 )
Recent downloads (6 months)1 ( #181,202 of 1,692,585 )
How can I increase my downloads?