Universality in Set Theories

Universality in Set Theories
Author: Manuel Bremer
Publisher: Walter de Gruyter
Total Pages: 125
Release: 2013-05-02
Genre: Philosophy
ISBN: 3110326108

The book discusses the fate of universality and a universal set in several set theories. The book aims at a philosophical study of ontological and conceptual questions around set theory. Set theories are ontologies. They posit sets and claim that these exhibit the essential properties laid down in the set theoretical axioms. Collecting these postulated entities quantified over poses the problem of universality. Is the collection of the set theoretical entities itself a set theoretical entity? What does it mean if it is, and what does it mean if it is not? To answer these questions involves developing a theory of the universal set. We have to ask: Are there different aspects to universality in set theory, which stand in conflict to each other? May inconsistency be the price to pay to circumvent ineffability? And most importantly: How far can axiomatic ontology take us out of the problems around universality?

Set Theory with a Universal Set

Set Theory with a Universal Set
Author: T. E. Forster
Publisher:
Total Pages: 0
Release: 2023
Genre: Set theory
ISBN: 9781383022636

This updated edition offers the reader an introduction to the field, which focuses on Quine's original work. It includes a revised account of the set theories of Church-Oswald and Mitchell, with permutation models and extensions that preserve power sets.

A Book of Set Theory

A Book of Set Theory
Author: Charles C Pinter
Publisher: Courier Corporation
Total Pages: 259
Release: 2014-07-23
Genre: Mathematics
ISBN: 0486497089

"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

Principia Mathematica

Principia Mathematica
Author: Alfred North Whitehead
Publisher:
Total Pages: 688
Release: 1910
Genre: Logic, Symbolic and mathematical
ISBN:

Basic Category Theory

Basic Category Theory
Author: Tom Leinster
Publisher: Cambridge University Press
Total Pages: 193
Release: 2014-07-24
Genre: Mathematics
ISBN: 1107044243

A short introduction ideal for students learning category theory for the first time.

Sets for Mathematics

Sets for Mathematics
Author: F. William Lawvere
Publisher: Cambridge University Press
Total Pages: 280
Release: 2003-01-27
Genre: Mathematics
ISBN: 9780521010603

In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.

An Invitation to General Algebra and Universal Constructions

An Invitation to General Algebra and Universal Constructions
Author: George M. Bergman
Publisher: Springer
Total Pages: 574
Release: 2015-02-05
Genre: Mathematics
ISBN: 3319114786

Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.

Fundamentals of Set and Number Theory

Fundamentals of Set and Number Theory
Author: Valeriy K. Zakharov
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 448
Release: 2018-02-05
Genre: Mathematics
ISBN: 3110550946

This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory Compactness theorem for generalized second-order language

ROUGH NEUTROSOPHIC RELATION ON TWO UNIVERSAL SETS

ROUGH NEUTROSOPHIC RELATION ON TWO UNIVERSAL SETS
Author: I. AROCKIARANI
Publisher: Infinite Study
Total Pages: 14
Release:
Genre:
ISBN:

In this paper, we define the rough neutrosophic relation of two universe sets and study the algebraic properties of two rough neutrosophic relations that are interesting in the theory of rough sets. Finally, we present the similarity rough neutrosophic relation with an example.

Classical Descriptive Set Theory

Classical Descriptive Set Theory
Author: Alexander Kechris
Publisher: Springer Science & Business Media
Total Pages: 419
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461241901

Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.