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Lectures in Logic and Set Theory. Volume 2 -- Set Theory.pdf
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CAMBRIDGE STUDIES IN
ADVANCED MATHEMATICS
EDITORIAL BOARD
B. BOLLOBAS, W. FULTON, A. KATOK, F. KIRWAN,
P. SARNAK
Lectures in Logic and Set Theory Volume 2
This two-volume work bridges the gap between introductory expositions of
logic or set theory on one hand, and the research literature on the other. It can
be used as a text in an advanced undergraduate or beginning graduate course
in mathematics, computer
science, or philosophy. The
volumes are written in
a user-friendly conversational lecture style that makes them equally effective
for self-study or class use.
Volume 2, on formal (ZFC) set theory, incorporates a self-contained
“Chapter 0” on proof techniques so that it is based on formal logic, in the style
of Bourbaki. The emphasis on basic techniques will provide the reader with
a solid foundation in set theory and sets a context for the presentation of ad-
vanced
topics such as absoluteness, relati
ve consistency results, tw
o exposi-
tions of G¨odel’s constructible universe, numerous ways of viewing recursion,
and a chapter on Cohen forcing.
George Tourlakis is Professor of Computer Science at York University of
Ontario.

Already published
2 K. Petersen Ergodic theory
3 P.T. Johnstone Stone spaces
5 J.-P. Kahane Some random series of functions, 2nd edition
7 J. Lambek & P.J. Scott Introduction to higher-order categorical logic
8 H. Matsumura Commutative ring theory
10 M. Aschbacher Finite group theory, 2nd edition
11 J.L. Alperin Local representation theory
12 P. Koosis The logarithmic integral I
14 S.J. Patterson An introduction to the theory of the Riemann zeta-function
15 H.J. Baues Algebraic homotopy
16 V.S. Varadarajan Introduction to harmonic analysis on semisimple Lie groups
17 W. Dicks & M. Dunwoody Groups acting on graphs
19 R. Fritsch & R. Piccinini Cellular structures in topology
20 H. Klingen Introductory lectures on Siegel modular forms
21 P. Koosis The logarithmic integral II
22 M.J. Collins Representations and character
s of finite groups
24 H. Kunita Stochastic flows and stochastic
differential equations
25
P. Wojtaszczyk
Banac
h spaces for analysts
26 J.E. Gilbert & M.A.M. Murray Clifford algebras and Dirac
operators in harmonic analysis
27 A. Frohlich & M.J. Taylor Algebraic number theory
28 K. Goebel & W.A. Kirk Topics in metric fixed point theory
29 J.F. Humphreys Reflection groups and Coxeter groups
30 D.J. Benson Representations and cohomology I
31 D.J. Benson Representations and cohomology II
32 C. Allday & V. Puppe Cohomological methods in transformation groups
33 C. Soule et al. Lectures on Arakelov geometry
34 A. Ambrosetti & G. Prodi A primer of nonlinear analysis
35 J. Palis & F. Takens Hyperbolicity, stability and chaos at homoclinic bifurcations
37 Y. Meyer Wavelets and operators 1
38 C. Weibel, An introduction to homological algebra
39 W. Bruns & J. Herzog Cohen-Macaulay rings
40 V. Snaith Explicit Brauer induction
41 G. Laumon Cohomology of Drinfeld modular varieties I
42 E.B. Davies Spectral theory and differential operators
43 J. Diestel, H. Jarchow, & A. Tonge Absolutely summing operators
44 P. Mattila Geometry of sets and measures in Euclidean spaces
45 R. Pinsky Positive harmonic functions and diffusion
46 G. Tenenbaum Introduction to analytic and probabilistic number theory
47 C. Peskine An algebraic introduction to complex projective geometry
48 Y. Meyer & R. Coifman Wavelets
49 R. Stanley Enumerative combinatorics I
50 I. Porteous Clifford algebras and the classical groups
51 M. Audin Spinning tops
52 V. Jurdjevic Geometric control theory
53 H. Volklein Groups as Galois groups
54 J. Le Potier Lectures on vector bundles
55 D. Bump Automorphic forms and representations
56 G. Laumon Cohomology of Drinfeld modular varieties II
57 D.M. Clark & B.A. Davey Natural dualities for the working algebraist
58 J. McCleary A user’s guide to spectral sequences II
59 P. Taylor Practical foundations of mathematics
60 M.P. Brodmann & R.Y. Sharp Local cohomology
61 J.D. Dixon et al. Analytic pro-P groups
62 R. Stanley Enumerative combinatorics II
63 R.M. Dudley Uniform central limit theorems
64 J. Jost & X. Li-Jost Calculus of variations
65 A.J. Berrick & M.E. Keating An introduction to rings and modules
66 S. Morosawa Holomorphic dynamics
67 A.J. Berrick & M.E. Keating Categories and modules with K-theory in view
68 K. Sato Levy processes and infinitely divisible distributions
69 H. Hida Modular forms
and Galois cohomology
70 R. Iorio & V. Iorio Fourier analysis and
partial differential equations
71 R. Blei Analysis in integer and fractional dimensions
72 F. Borceaux & G. Janelidze Galois theories
73 B. Bollobas Random graphs

LECTURES IN LOGIC
AND SET THEORY
Volume 2: Set Theory
GEORGE TOURLAKIS
York University
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