Descriptive Dynamics

The purpose of the following informal lectures is to give a brief introduction to descriptive dynamics, which I understand here to be the descriptive theory of Polish group actions. I will concentrate on the foundations, and hopefully at a level accessible to anyone with a basic knowledge of descriptive set theory. I will illustrate some of the main methods used in this area, including Baire category arguments and various implementations of the "changing the topology" technique. A general reference for the results discussed in this paper is Becker-Kechris [1996]

Third-order matching in λ→\lambda\rightarrow-Curry is undecidable

Given closed untyped $\lambda$-terms $\lambda x1... xk.s$ and $t$, which can be assigned some types $S1->...->Sk->T$ and $T$ respectively in the Curry-style systems of type assignment (essentially due to R.~Hindley) $\lambda->$-Curry [Barendregt 92], $\lambda^{->}_t$ [Mitchell 96], $TA_\lambda$ [Hindley97], it is undecidable whether there exist closed terms $s1,...,sk$ of types $S1,...,Sk$ such that $s[s1/x1,...,sk/xk]=_{\beta\eta}t$, even if the orders of $si$'s do not exceed 3. This undecidability result should be contrasted to the decidability of the third-order matching in the Church-style simply typed lambda calculus with a single constant base type [Dowek 92]. The proof is by reduction from the recursively inseparable sets of invalid and finitely satisfiable sentences of the first-order theory of binary relation [Trakhtenbrot 53, Vaught 60]

Notions of Relative Ubiquity for Invariant Sets of Relational Structures

Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers w as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on w. For example, in every sense of relative ubiquity considered here, the set of dense linear orderings on w is ubiquitous in the set of linear orderings on w

Analytic Equivalence Relations and Ulm-Type Classifications

Our main goal in this paper is to establish a Glimm-Effros type dichotomy for arbitrary analytic equivalence relations

October 2, 1976 Football Program, UOP vs. Long Beach State

https://scholarlycommons.pacific.edu/ua-football/1394/thumbnail.jp

New Mexico State Record, 03-11-1921

https://digitalrepository.unm.edu/nm_state_record_news/1243/thumbnail.jp

Towards establishing an epistemological position for library and information science

Bibliography: leaves 497-531.This study examines the need for and value of a theory of knowledge for library and information science that would account for the 'Ways in which given philosophical assumptions lead to certain modes of professional practice and styles of academic research. Since given theoretical standpoints influence the nature of library practice and tend to structure the way in which library and information science research is conducted, this investigation focuses on an analysis of the fundamental conceptions of knowledge, information, truth and reality in the context of the unique complex of functions of this profession. The main method applied in this study is a representative consultation and review of the literatures of library and information science, and of a few cognate or classical fields of study. A special focus is the examination and analysis of the writings of more than 40 selected library and information science theorists, as well as those of non-librarians. The inductively-derived results of this examination are reflected in analytical typologies. The holistic intellectual tradition that underlies the presumed continuities and commonalities in the typologies is developed as a framework for developing suitable criteria to establish and evaluate an appropriate epistemological position for library and information science. An epistemological position called holistic perspectivism is proposed as one which satisfies the postulated criteria. A graphic model of this position is explained as a means of demonstrating the application of holistic perspectivism in given areas of the knowledge-transfer role of library and information science