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ARE WE CLOSER TO A SOLUTION OF THE CONTINUUM PROBLEM?
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Palavras-chave

Axiomatic Set Theory. Continuum Hypothesis. Independence of the continuum hypothesis. Large cardinals. Forcing. Determinacy

Como Citar

DI PRISCO, Carlos Augusto. ARE WE CLOSER TO A SOLUTION OF THE CONTINUUM PROBLEM?. Manuscrito: Revista Internacional de Filosofia, Campinas, SP, v. 28, n. 2, p. 331–350, 2016. Disponível em: https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8643921. Acesso em: 19 abr. 2024.

Resumo

The Continuum Hypothesis has motivated a considerable part of the development of axiomatic set theory for over a century. We present, in a very schematic way, some of the results that give information related to Cantor’s Continuum Problem.
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Referências

BAGARIA, J. The many faces of the continuum. A short introductory

course on the set theory of the continuum, 1998.

BAGARIA, J. “Natural axioms of set theory and the continuum problem”.

In: P. Hajek, L. Vald´es Villanueva and D. Westerst˚ahl (eds.). Logic, Methodology and Philosophy of Science, Proceedings of the International Congress. King’s College Publications, 2005.

COHEN, P.J. “The independence of the continuum hypothesis”.Proceedings of the National Academy of Sciences, U.S.A., 50, 1963, and 51, 1964.

FEFERMAN, S., FRIEDMAN, H., MADDY, P. and STEEL, J. “Does mathematics need new axioms?”. The Bulletin of Symbolic Logic, 6, pp. 401-446, 2000.

FOREMAN, M. “Generic large cardinals: New axioms for mathematics?”

Proceedings of the International Congress of Mathematicians, vol. II. Berlin, pp. 1-21, 1998.

FOREMAN, M., MAGIDOR, M. and SHELAH, S. “Martin’s maximum, saturated ideals and non regular ultrafilters I”’. Ann. of Math., 127, pp. 1-47, 1988.

FREMLIN, D. Consequences of Martin’s Axiom. Cambridge: Cambridge

University Press, 1984.

GODEL, K. “The consistency of the axiom of choice and the gener- ¨

alized continuum hypothesis”. Proc. Natl. Acad. Sci., 24, pp. 556-557, 1938.

GODEL, K. “What is Cantor’s continuum problem?”. ¨ American Mathematical Monthly, 54, pp. 515-525, 1947. Repr. in P. Benacerraf

and H. Putnam (eds.). Cambridge: Cambridge University Press, 1983.

GODEL, K. “Some considerations leading to the probable conclusion ¨

that the true power of the continuum is ℵ2”. In K. G¨odel Collected

Works, vol. 3. S. Feferman, J. Dawson Jr., W. Goldfarb, C. Parsons and R. Solovay (eds.). Oxford: Oxford University Press, 2001.

JECH, T. Set Theory. Springer-Verlag, 2003.

KANAMORI, A. The Higher Infinite. Berlin: Springer-Verlag, 1994.

KUNEN, K. Set Theory: An introduction to independence proofs. Amsterdam: North Holland, 1980.

MARTIN, D.A. “Measurable cardinals and analytic games”. Fund. Math., 66, pp. 287-291, 1970.

MARTIN, D.A. “Borel determinacy”. Ann. of Math., 102, pp. 363-371, 1975.

SHELAH, S. and WOODIN, W.H. “Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable”. Israel Journal of Mathematics, 70, pp. 381-394, 1990.

SOLOVAY, R. “On the cardinality of Σ12 sets of reals”. In Foundations

of Mathematics (Symposium commemotaring Kurt G¨odel, Colombus, Ohio, 1966). Berlin: Springer, pp. 58-73, 1969.

TODORCEVIC, S. “Generic absoluteness and the continuum”. Mathematical Research Letters, 9, pp. 465-472, 2002.

WOODIN, W. H. “The Continuum Hypothesis”. Notices of the Amer.

Math, Soc., 48, 2001. Part I, pp. 567-576. Part II, pp. 681-690.

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