Σ31-Absoluteness for Sequences of Measures
We extend Jensen’s Σ 3 1 -absoluteness result to apply to the core model for sequences of measures, provided that sharps exist and there is no inner model of ∃ko(k) = k ++. The proof includes a result on the patterns of indiscernibles analogous to the one which arises in Jensen’s proof.
KeywordsInitial Segment Accumulation Point Core Model Order Type Total Measure
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- [Dod82]A. Dodd, The Core Model, London Math. Soc. Lecture Notes Gl, Cambridge University Press, Cambridge, 1982.Google Scholar
- [Jen81]R. Jensen, Some Applications of the Core Model, Set Theory and Model Theory, Lecture Notes in Mathematics 872 (B. Jensen and A. Prestel, eds.), Springer-Verlag, New York, 1981, pp. 55–97.Google Scholar
- [Mi84]W. J. Mitchell, The Core Model for Sequences of Measures, I, Math. Proc. of the Cambridge Philosophical Society 95 (1984), 41–58.Google Scholar
- [Mi]W. J. Mitchell, The Core Model for Sequences of Measures, II, submitted to Math. Proc. of the Cambridge Phil. Soc. Google Scholar
- [Mi91a]W. J. Mitchell, On the Singular Cardinal Hypothesis, Transactions of the American Mathematical Society (to appear).Google Scholar
- [Mi91b]W. J. Mitchell, Definable Singularity, Transactions of the American Mathimatical Society (to appear).Google Scholar
- [MiS89]W. J. Mitchell and J. Steel, Fine Structure and Iteration Trees, (in preparation).Google Scholar
- [Sho61]J. R. Shoenfield, The Problem of Predicativity, Essays on the Foundations of Mathematics (Y. Bar-Hillel, E. I. J Poznanski, M. O. Rabin and A. Robinson, eds.), The Magnes Press, Jerusalem, 1961, pp. 132–142.Google Scholar
- [Ste90]J. Steel, The Core Model Iterability Problem, Handwritten notes (June 1990).Google Scholar