Atnaujinkite slapukų nuostatas

El. knyga: Set Theory and its Philosophy: A Critical Introduction

3.78/5 (53 ratings by Goodreads)
(, Department of Philosophy, University of Cambridge)
  • Formatas: PDF+DRM
  • Išleidimo metai: 15-Jan-2004
  • Leidėjas: Oxford University Press
  • Kalba: eng
  • ISBN-13: 9780191556432
Kitos knygos pagal šią temą:
Set Theory and its Philosophy: A Critical IntroductionDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Išleidimo metai: 15-Jan-2004
  • Leidėjas: Oxford University Press
  • Kalba: eng
  • ISBN-13: 9780191556432
Kitos knygos pagal šią temą:

DRM apribojimai

  • Kopijuoti:

    neleidžiama

  • Spausdinti:

    neleidžiama

  • El. knygos naudojimas:

    Skaitmeninių teisių valdymas (DRM)
    Leidykla pateikė šią knygą šifruota forma, o tai reiškia, kad norint ją atrakinti ir perskaityti reikia įdiegti nemokamą programinę įrangą. Norint skaityti šią el. knygą, turite susikurti Adobe ID . Daugiau informacijos  čia. El. knygą galima atsisiųsti į 6 įrenginius (vienas vartotojas su tuo pačiu Adobe ID).

    Reikalinga programinė įranga
    Norint skaityti šią el. knygą mobiliajame įrenginyje (telefone ar planšetiniame kompiuteryje), turite įdiegti šią nemokamą programėlę: PocketBook Reader (iOS / Android)

    Norint skaityti šią el. knygą asmeniniame arba „Mac“ kompiuteryje, Jums reikalinga  Adobe Digital Editions “ (tai nemokama programa, specialiai sukurta el. knygoms. Tai nėra tas pats, kas „Adobe Reader“, kurią tikriausiai jau turite savo kompiuteryje.)

    Negalite skaityti šios el. knygos naudodami „Amazon Kindle“.

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Recenzijos

a wonderful new book . . . Potter has written the best philosophical introduction to set theory on the market * Timothy Bays, Notre Dame Philosophical Reviews *

I Sets
1(78)
Introduction to Part I
3(3)
Logic
6(15)
The axiomatic method
6(5)
The background logic
11(2)
Schemes
13(3)
The choice of logic
16(2)
Definite descriptions
18(3)
Notes
20(1)
Collections
21(13)
Collections and fusions
21(2)
Membership
23(2)
Russell's paradox
25(1)
Is it a paradox?
26(1)
Indefinite extensibility
27(3)
Collections
30(4)
Notes
32(2)
The hierarchy
34(21)
Two strategies
34(2)
Construction
36(2)
Metaphysical dependence
38(2)
Levels and histories
40(2)
The axiom scheme of separation
42(1)
The theory of levels
43(4)
Sets
47(3)
Purity
50(1)
Well-foundedness
51(4)
Notes
53(2)
The theory of sets
55(24)
How far can you go?
55(2)
The initial level
57(1)
The empty set
58(2)
Cutting things down to size
60(1)
The axiom of creation
61(2)
Ordered pairs
63(2)
Relations
65(2)
Functions
67(1)
The axiom of infinity
68(4)
Structures
72(4)
Notes
75(1)
Conclusion to Part I
76(3)
II Numbers
79(72)
Introduction to Part II
81(7)
Arithmetic
88(15)
Closure
88(1)
Definition of natural numbers
89(3)
Recursion
92(3)
Arithmetic
95(3)
Peano arithmetic
98(5)
Notes
101(2)
Counting
103(14)
Order relations
103(3)
The ancestral
106(2)
The ordering of the natural numbers
108(2)
Counting finite sets
110(3)
Counting infinite sets
113(1)
Skolem's paradox
114(3)
Notes
116(1)
Lines
117(12)
The rational line
117(2)
Completeness
119(2)
The real line
121(4)
Souslin lines
125(1)
The Baire line
126(3)
Notes
128(1)
Real numbers
129(22)
Equivalence relations
129(1)
Integral numbers
130(2)
Rational numbers
132(3)
Real numbers
135(1)
The uncountability of the real numbers
136(2)
Algebraic real numbers
138(2)
Archimedean ordered fields
140(4)
Non-standard ordered fields
144(5)
Notes
147(2)
Conclusion to Part II
149(2)
III Cardinals and Ordinals
151(56)
Introduction to Part III
153(2)
Cardinals
155(12)
Definition of cardinals
155(2)
The partial ordering
157(2)
Finite and infinite
159(2)
The axiom of countable choice
161(6)
Notes
165(2)
Basic cardinal arithmetic
167(8)
Finite cardinals
167(1)
Cardinal arithmetic
168(2)
Infinite cardinals
170(2)
The power of the continuum
172(3)
Notes
174(1)
Ordinals
175(16)
Well-ordering
175(4)
Ordinals
179(3)
Transfinite induction and recursion
182(2)
Cardinality
184(2)
Rank
186(5)
Notes
189(2)
Ordinal arithmetic
191(16)
Normal functions
191(1)
Ordinal addition
192(4)
Ordinal multiplication
196(3)
Ordinal exponentiation
199(3)
Normal form
202(3)
Notes
204(1)
Conclusion to Part III
205(2)
IV Further Axioms
207(82)
Introduction to Part IV
209(2)
Orders of infinity
211(27)
Goodstein's theorem
212(6)
The axiom of ordinals
218(3)
Reflection
221(4)
Replacement
225(2)
Limitation of size
227(3)
Back to dependency?
230(1)
Higher still
231(3)
Speed-up theorems
234(4)
Notes
236(2)
The axiom of choice
238(23)
The axiom of countable dependent choice
238(2)
Skolem's paradox again
240(2)
The axiom of choice
242(1)
The well-ordering principle
243(2)
Maximal principles
245(5)
Regressive arguments
250(2)
The axiom of constructibility
252(4)
Intuitive arguments
256(5)
Notes
259(2)
Further cardinal arithmetic
261(28)
Alephs
261(1)
The arithmetic of alephs
262(1)
Counting well-orderable sets
263(3)
Cardinal arithmetic and the axiom of choice
266(2)
The continuum hypothesis
268(2)
Is the continuum hypothesis decidable?
270(5)
The axiom of determinacy
275(5)
The generalized continuum hypothesis
280(4)
Notes
283(1)
Conclusion to Part IV
284(5)
Appendices
289(28)
A Traditional axiomatizations
291(8)
A.1 Zermelo's axioms
291(1)
A.2 Cardinals and ordinals
292(4)
A.3 Replacement
296(2)
Notes
298(1)
B Classes
299(13)
B.1 Virtual classes
300(2)
B.2 Classes as new entities
302(1)
B.3 Classes and quantification
303(3)
B.4 Classes quantified
306(1)
B.5 Impredicative classes
307(1)
B.6 Impredicativity
308(2)
B.7 Using classes to enrich the original theory
310(2)
C Sets and classes
312(5)
C.1 Adding classes to set theory
312(1)
C.2 The difference between sets and classes
313(2)
C.3 The metalinguistic perspective
315(1)
Notes
316(1)
References 317(12)
List of symbols 329(2)
Index of definitions 331(5)
Index of names 336


Michael Potter is University Lecturer in Philosophy, and Fellow of Fitzwilliam College, at Cambridge. He is the author of Sets (1990), on which the present work draws but which was written for a more specialist readership, and Reason's Nearest Kin (2000).
Daugiau apie elektronines knygas Daugiau apie elektronines knygas
Pastovi nuoroda: https://www.kriso.lt/db/97801915564322e.html
Raktažodžiai: