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A Universal Separable Diversity

100%

Bryant D., Nies A., Tupper P.

Analysis and Geometry in Metric Spaces

2017

tom 5

nr 1

138-151

The Urysohn space is a separable complete metric space with two fundamental properties: (a) universality: every separable metric space can be isometrically embedded in it; (b) ultrahomogeneity: every finite isometry between two finite subspaces can be extended to an auto-isometry of the whole space. The Urysohn space is uniquely determined up to isometry within separable metric spaces by these two properties. We introduce an analogue of the Urysohn space for diversities, a recently developed variant of the concept of a metric space. In a diversity any finite set of points is assigned a non-negative value, extending the notion of a metric which only applies to unordered pairs of points.We construct the unique separable complete diversity that it is ultrahomogeneous and universal with respect to separable diversities.

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Universality of Logic

72%

Woleński J.

Bulletin of the Section of Logic

2017

tom 46

nr 1/2

This paper deals with the problem of universality property of logic. At first, this property is analyzed in the context of first-order logic. Three senses of the universality property are distinguished: universal applicability, topical neutrality and validity (truth in all models). All theses senses can be proved to be justified. The fourth understanding, namely the amount of expressive power, is connected with the criticism of the first-order thesis: first-order logic is the logic. The categorical approach to logic is presented as associated with the last understanding of universality. The author concludes that two senses of universality should be sharply discriminated and defends the first-order thesis.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Bulletin of the Section of Logic

1 Bryant D.

1 Nies A.

1 Tupper P.

1 Woleński J.

2 2017

Wyniki wyszukiwania

A Universal Separable Diversity

Universality of Logic