This is a preview of subscription content, log in via an institution to check access.
REFERENCES
Abramson, F. G., L. A. Harrington, E. M. Kleinberg, and W. S. Zwicker: 1977, ‘Flipping Properties: A Unifying Thread in the Theory of Large Cardinals’, Annals of Mathematical Logic 12, 25–58.
Barnabel, J. B.: 1989, ‘Flipping Properties and Huge Cardinals’, Fundamenta Mathematicae 132, 171–188.
Cohen, P.: 1963, ‘The Independence of the Continuum Hypothesis’, Proceedings of the National Academy of Sciences of the United States of America 50, 1143–1148.
Devlin, K. J.: 1984, Constructibility, Berlin [Perspectives in Mathematical Logic].
Di Prisco, C. A. and W. Marek: 1985, ‘Some Aspects of the Theory of Large Cardinals’, in L. P. de Alcantara (ed.), Mathematical Logic and Formal Systems, A Collection of Papers in Honor of Newton C. A. da Costa, New York, pp. 87–139. [Lecture Notes in Pure and Applied Mathematics 94]
Di Prisco, C. A. and W. S. Zwicker: 1980, ‘Flipping Properties and Supercompact Cardinals’, Fundamenta Mathematicae 109, 31–36.
Dougherty, R. and T. Jech: 1997, ‘Finite Left-distributive Algebras and Embedding Algebras’, Advances in Mathematics 130, 201–291.
Gaifman, H.: 1974, ‘Elementary Embeddings of Set Theory and Certain Subtheories’, in T. Jech (ed.), Axiomatic Set Theory, Proceedings of the Symposium in Pure Mathem-atics of the American Mathematical Society, held at the University of California, Los Angeles, Calif., July 10—August 5, 1967, Providence [Proceedings of Symposia in Pure Mathematics, XIII, Part II], 33–101.
Gale, D. and F. M. Stewart: 1953, ‘Infinite Games with Perfect Information’, in H. W. Kuhn and A.W. Tucker(eds.),Contributions to the Theory of Games II, Princeton [Annals of Mathematical Studies 28], 245–266.
Gödel, K.: 1931, ‘Ñber formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I’, Monatshefte für Mathematik und Physik 38, 173–198.
Gödel, K.: 1938, ‘The Consistency of the Axiom of Choice and of the Generalized Continuum-hypothesis’, Proceedings of the National Academy of Sciences of the United States of America 24, 556–557.
Hausdorff, F. (Paul Mongré): 1898, Das Chaos in kosmischer Auslese — Ein erkenntniskri-tischer Versuch,Leipzig.
Jech, T.: 1978, Set Theory, San Diego.
Kanamori, A.: 1994, The Higher Infinite, Large Cardinals in Set Theory from Their Beginnings, Berlin [Perspectives in Mathematical Logic].
Kanamori, A. and M. Magidor: 1978, ‘The Evolution of Large Cardinal Axioms in Set Theory’, in G. H. Müller and D. S. Scott (eds.), Higher Set Theory, Proceedings, Oberwolfach, Germany, April 13–23, 1977, Berlin [Lecture Notes in Mathematics 669], 99–275.
Koepke, P.: 1996, ‘Embedding Normal Forms and \(\Pi _1^1 \)-determinacy, in W. Hodges, M. Hyland, C. Steinhorn and J. K. Truss (eds), Logic: From Foundations to Applications, European Logic Colloquium, Keele, UK, July 20–29, 1993, Oxford, 215–224.
Koepke, P.: 1998, ‘Extenders, Embedding Normal Forms, and the Martin—Steel-theorem’, Journal of Symbolic Logic 63, 1137–1176.
Laver, R.: 1992, ‘The Left Distributive Law and the Freeness of an Algebra of Elementary Embeddings’, Advances in Mathematics 91, 209–231.
Laver, R.: 1997, ‘Implications between Strong Large Cardinal Axioms’, Annals of Pure and Applied Logic 90, 79–90.
Martin, D. A.: 1970, ‘Measurable Cardinals and Analytic Games’, Fundamenta Mathematicae 66, 287–291.
Martin, D. A. and J. R. Steel: 1989, ‘A Proof of Projective Determinacy’, Journal of the American Mathematical Society 2, 71–125.
Moschovakis, Y. N.: 1980, Descriptive Set Theory, Amsterdam [Studies in Logic and the Foundations of Mathematics 100].
Scott, D.: 1961, ‘Measurable Cardinals and Constructible Sets’, Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques 9, 521–524.
Shelah, S. and W. H. Woodin: 1990, ‘Large Cardinals Imply that Every Reasonably Definable Set of Reals is Lebesgue Measurable’, Israel Journal of Mathematics 70, 381–394.
Tarski, A.: 1935, ‘Der Wahrheitsbegriff in den formalisierten Sprachen’, Studia Philosophica 1, 261–405.
Ulam, S.: 1930, ‘Zur Maßtheorie in der allgemeinen Mengenlehre’, Fundamenta Mathematicae 16, 140–150.
von Neumann, J.: 1923, ‘Zur Einführung der transfiniten Zahlen’, Acta Universitatis Szegediensis, Sectio Scientiarum Mathematicarum 1, 199–208.
von Neumann, J.: 1925, ‘Eine Axiomatisierung der Mengenlehre’, Journal für die reine und angewandte Mathematik 154, 219–240.
Zermelo, E.: 1904, ‘Beweis, dass jede Menge wohlgeordnet werden kann (Aus einem an Herrn Hilbert gerichteten Briefe)’, Mathematische Annalen 59, 139–141.
Zermelo, E.: 1930, ‘Ñber Grenzzahlen und Mengenbereiche: Neue Untersuchungen über die Grundlagen der Mengenlehre’, Fundamenta Mathematicae 16, 29–47.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Koepke, P. The Category of Inner Models. Synthese 133, 275–303 (2002). https://doi.org/10.1023/A:1020818827349
Issue Date:
DOI: https://doi.org/10.1023/A:1020818827349