The Mathematical Experience |
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Page 231
... restricted set theory is consistent , then so is standard set theory ( or nonstandard theory ) . Gödel's idea was to construct a model for restricted set theory , and to prove that in this model the axiom of choice and the continuum ...
... restricted set theory is consistent , then so is standard set theory ( or nonstandard theory ) . Gödel's idea was to construct a model for restricted set theory , and to prove that in this model the axiom of choice and the continuum ...
Page 232
... restricted set theory already are self - contradictory . Any contradiction they cause must already be present in con- structible set theory , which is a model for ordinary set the- ory . In other words , it was known that neither could ...
... restricted set theory already are self - contradictory . Any contradiction they cause must already be present in con- structible set theory , which is a model for ordinary set the- ory . In other words , it was known that neither could ...
Page 233
... restricted set theory to construct a model in which the negation of the axiom of choice or the negation of the continuum hypothesis can be proved as theorems . It ... theory : uniting two or more sets to form 233 Non - Cantorian Set Theory.
... restricted set theory to construct a model in which the negation of the axiom of choice or the negation of the continuum hypothesis can be proved as theorems . It ... theory : uniting two or more sets to form 233 Non - Cantorian Set Theory.
Other editions - View all
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience, Study Edition Philip Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 2011 |
The Mathematical Experience: Study Edition Philip J. Davis,Reuben Hersh,Elena Anne Marchisotto Limited preview - 1995 |
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abstract aesthetic algebra algorithmic analysis analytic answer applications argument arithmetic asserts axiom of choice Bibliography calculus called century circle complex conjecture construct continuum hypothesis course definition differential equations elements ematics Euclid Euclidean geometry Euler example existence experience fact figure finite formal language formalist formula Fourier Fourier series function Further Readings G. H. Hardy Hilbert human hypercube hypersquares idea ideal infinite set infinitesimal infinity integers intuition knowledge Lakatos logic mathe mathematical objects mathematical proof mathematicians matics means ment method natural numbers non-Euclidean geometry non-Riemannian nonstandard notion number theory parallel postulate philosophy of mathematics physical Platonism Platonist possible postulate prime number prime number theorem problem proof proved question real numbers reason restricted set theory result rigorous sense solution square statement straight line symbols theorem thing tion triangle true truth universe words zero