The Category of Inner Models

A partir des techniques de la theorie des grands nombres cardinaux, l'A. examine la categorie de modele interne et en mesure les consequences sur la theorie des ensembles de Zermelo-Fraenkel. Soulevant la question philosophique des mondes possibles en termes de morphismes, l'A. montre que les modeles internes et les enchâssements elementaires manifestent des proprietes structurelles pertinentes pour la theorie descriptiviste des ensembles.

[1]  Alfred Tarski,et al.  Der Wahrheitsbegriff in den formalisierten Sprachen , 1935 .

[2]  Richard Laver Implications Between Strong Large Cardinal Axioms , 1997, Ann. Pure Appl. Log..

[3]  Donald A. Martin,et al.  Measurable cardinals and analytic games , 2003 .

[4]  Matthew Foreman Review: Donald A. Martin, John R. Steel, Projective Determinacy; W. Hugh Woodin, Supercompact Cardinals, Sets of Reals, and Weakly Homogeneous Trees; Donald A. Martin, John R. Steel, A Proof of Projective Determinacy , 1992 .

[5]  Saharon Shelah,et al.  Large cardinals imply that every reasonably definable set of reals is lebesgue measurable , 1990 .

[6]  Julius B. Barbanel Flipping properties and huge cardinals , 1989 .

[7]  E. Zermelo Über Grenzzahlen und Mengenbereiche , 1930 .

[8]  A. Kanamori The higher infinite : large cardinals in set theory from their beginnings , 2005 .

[9]  J. Neumann,et al.  Die Axiomatisierung der Mengenlehre , 1928 .

[10]  K. Gödel Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I , 1931 .

[11]  Y. Moschovakis Descriptive Set Theory , 1980 .

[12]  S. Ulam,et al.  Zur Masstheorie in der allgemeinen Mengenlehre , 1930 .

[13]  William S. Zwicker,et al.  Flipping properties: A unifying thread in the theory of large cardinals , 1977 .

[14]  J. Neumann Eine Axiomatisierung der Mengenlehre. , 1925 .

[15]  Donald A. Matrin Measurable cardinals and analytic games , 1970 .

[16]  Akihiro Kanamori,et al.  The evolution of large cardinal axioms in set theory , 1978 .

[17]  Thomas Jech,et al.  Finite Left-Distributive Algebras and Embedding Algebras , 1997 .

[18]  E. Zermelo Beweis, daß jede Menge wohlgeordnet werden kann , 1904 .

[19]  Richard Laver,et al.  The Left Distributive Law and the Freeness of an Algebra of Elementary Embeddings , 1992 .

[20]  John R. Steel,et al.  A proof of projective determinacy , 1989 .

[21]  Dana Scott Measurable Cardinals and Constructible Sets , 2003 .

[22]  A. Fraenkel Untersuchungen über die Grundlagen der Mengenlehre , 1925 .

[23]  W. Szymanowski,et al.  BULLETIN DE L'ACADEMIE POLONAISE DES SCIENCES , 1953 .

[24]  K. Gödel The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis. , 1938, Proceedings of the National Academy of Sciences of the United States of America.

[25]  Wilfrid Hodges,et al.  Logic: from foundations to applications: European logic colloquium , 1996 .

[26]  William S. Zwicker,et al.  Flipping properties and supercompact cardinals , 1980 .

[27]  Peter Koepke Extenders, Embedding Normal Forms, and the Martin-Steel-Theorem , 1998, J. Symb. Log..