Axiomatic Set Theory, Part 1 (Google eBook)

Front Cover
Dana S. Scott, Thomas J. Jech
American Mathematical Soc., 1971 - Mathematics - 474 pages
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Contents

SETS CONSTRUCTIBLE USING L
1
COMMENTS ON THE FOUNDATIONS OF SET THEORY
9
UNSOLVED PROBLEMS IN SET THEORY
17
A MORE EXPLICIT SET THEORY╣
49
SETS SEMISETS MODELS
67
THE BOOLEAN PRIME IDEAL THEOREM DOES NOT IMPLY THE AXIOM OF CHOICE
83
ON MODELS FOR SET THEORY WITHOUT AC
135
PRIMITIVE RECURSIVE SET FUNCTIONS
143
PREDICATIVE CLASSES
247
ON SOME CONSEQUENCES OF THE AXIOM OF DETERMINATENESS
265
EMBEDDING CLASSICAL TYPE THEORY IN INTUITIOMSTIC TYPE THEORY
267
ORDINAL DEFINABILITY
271
AN AXIOM OF STRONG INFINITY AND ANALYTIC HIERARCHY OF ORDINAL NUMBERS
279
LIBERAL INTUITIONISM AS A BASIS FOR SET THEORY
321
FORCING WITH PERFECT CLOSED SETS
331
UNRAMIFIED FORCING╣
357

END EXTENSIONS OF MODELS OF SET THEORY
177
OBSERVATIONS ON POPULAR DISCUSSIONS OF FOUNDATIONS
189
INDESCRIBABILITY AND THE CONTINUUM
199
THE SIZES OF THE INDESCRIBABLE CARDINALS
205
ON THE LOGICAL COMPLEXITY OF SEVERAL AXIOMS OF SET THEORY
219
CATEGORICAL ALGEBRA AND SETTHEORETIC FOUNDATIONS
231
THE SOLUTION OF ONE OF ULAMS PROBLEMS CONCERNING ANALYTIC RECTANGLES
241
THE CONSISTENCY OF THE GCH WITH THE EXISTENCE OF A MEASURABLE CARDINAL
391
REALVALUED MEASURABLE CARDINALS╣
397
TRANSFINITE SEQUENCES OF AXIOM SYSTEMS FOR SET THEORY
429
HYPOTHESES ON POWER SET
439
MULTIPLE CHOICE AXIOMS
447
Author Index
467
Copyright

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Page 15 - ... into the unsafe ground of set theory. This is our fate, to live with doubts, to pursue a subject whose absoluteness we are not certain of, in short to realize that the only "true" science is itself of the same mortal, perhaps empirical, nature as all other human undertakings.
Page 11 - Platonist] position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.
Page 9 - The authors would like to acknowledge the support of the Air Force Office of Scientific Research through the program, "Theoretical and Experimental Studies of Vibroacoustic Systems", under the management of Major Brian Sanders. 1. Clark, RL and Fuller, CR, "Optimal placement of piezoelectric actuators and polyvinylidene fluoride error sensors in active structural acoustic control approaches,
Page 11 - To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hubert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency. . . . The Realist ] Platonist] position is probably the one which most mathematicians would prefer to take.

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