## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (198.174 recursos)

Notre Dame Journal of Logic

#### Mostrando recursos 1 - 5 de 5

Schroeder-Heister, Peter; Tranchini, Luca
Prawitz observed that Russell’s paradox in naive set theory yields a derivation of absurdity whose reduction sequence loops. Building on this observation, and based on numerous examples, Tennant claimed that this looping feature, or more generally, the fact that derivations of absurdity do not normalize, is characteristic of the paradoxes. Striking results by Ekman show that looping reduction sequences are already obtained in minimal propositional logic, when certain reduction steps, which are prima facie plausible, are considered in addition to the standard ones. This shows that the notion of reduction is in need of clarification. Referring to the notion of...
(application/pdf) - 03-oct-2017

2. #### Forking and Dividing in Henson Graphs

Conant, Gabriel
For $n\geq3$ , define $T_{n}$ to be the theory of the generic $K_{n}$ -free graph, where $K_{n}$ is the complete graph on $n$ vertices. We prove a graph-theoretic characterization of dividing in $T_{n}$ and use it to show that forking and dividing are the same for complete types. We then give an example of a forking and nondividing formula. Altogether, $T_{n}$ provides a counterexample to a question of Chernikov and Kaplan.
(application/pdf) - 03-oct-2017

3. #### Grades of Discrimination: Indiscernibility, Symmetry, and Relativity

Button, Tim
There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This paper aims to complete their technical investigation. Grades of indiscernibility are defined in terms of satisfaction of certain first-order formulas. Grades of symmetry are defined in terms of symmetries on a structure. Both of these families of grades of discrimination have been studied in some detail. However, this paper also introduces grades of relativity, defined in terms of relativeness correspondences. This paper explores the relationships...
(application/pdf) - 03-oct-2017

4. #### New Degree Spectra of Abelian Groups

Melnikov, Alexander G.
We show that for every computable ordinal of the form $\beta=\delta+2n+1\gt 1$ , where $\delta$ is zero or a limit ordinal and $n\in\omega$ , there exists a torsion-free abelian group having an $X$ -computable copy if and only if $X$ is nonlow $_{\beta}$ .
(application/pdf) - 03-oct-2017

5. #### Prospects for a Naive Theory of Classes

Field, Hartry; Lederman, Harvey; Øgaard, Tore Fjetland
The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are identical. In this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result...
(application/pdf) - 03-oct-2017

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