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Namba Forcing and No Good Scale

  • John Krueger (a1)

Abstract

We develop a version of Namba forcing which is useful for constructing models with no good scale on ℵ ω . A model is produced in which holds for all finite n ≥ 1, but there is no good scale on ℵ ω ; this strengthens a theorem of Cummings, Foreman, and Magidor [3] on the non-compactness of square.

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[1] Cummings, J., Notes on singular cardinal combinatorics, Notre Dame Journal of Formal Logic, vol. 46 (2005), no. 3, pp. 251282.
[2] Cummings, J., Foreman, M., and Magidor, M., Squares, scales, and stationary reflection, Journal of Mathematical Logic, vol. 1 (2001), no. 1, pp. 3598.
[3] Cummings, J., Foreman, M., and Magidor, M., The non-compactness of square, this Journal, vol. 68 (2003), no. 2, pp. 637643.
[4] Cummings, J., Foreman, M., and Magidor, M., Canonical structure in the universe of set theory. I, Annals of Pure and Applied Logic, vol. 129 (2004), no. 1-3, pp. 211243.
[5] Cummings, J., Foreman, M., and Magidor, M., Canonical structure in the universe of set theory. II, Annals of Pure and Applied Logic, vol. 142 (2006), no. 1-3, pp. 5575.
[6] Foreman, M. and Magidor, M., A very weak square principle, this Journal, vol. 62 (1997), no. 1, pp. 175196.
[7] Foreman, M., Magidor, M., and Shelah, S., Martins maximum, saturated ideals, andnonregular ultrafilters. I, Annals of Mathematics. Series 2, vol. 127 (1988), no. 2, pp. 147.
[8] Gitik, M. and Shelah, S., On the ⅈ-condition, Israel Journal of Mathematics, vol. 48 (1984), no. 2-3, pp. 148158.
[9] Hajnal, A., Juasz, I., and Shelah, S., Splitting strongly almost disjoint families, Transactions of the American Mathematical Society, vol. 295 (1986), no. 1, pp. 369387.
[10] Namba, K., Independence proof of (ω, ωα )-distributivity law in complete Boolean algebras, Com-mentarii Mathematici Universitatis Sancti Pauli, vol. 19 (1970), pp. 112.
[11] Shelah, S., Cardinal arithmetic, second ed., Oxford Logic Guides, vol. 29, The Clarendon Press, Oxford University Press, 1994.
[12] Shelah, S., Proper and improper forcing, second ed., Perspectives in Mathematical Logic, Springer Verlag, Berlin, 1998.

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