Remarks on Pκλ-combinatorics

• Autorzy: Shizuo Kamo
• Języki publikacji: EN

Abstrakty

EN

We prove that ${x ∈ P_κλ|x ∩ κ$ is almost x-ineffable} has $p_*(NIn_{κ, λ^{<κ}})$-measure 1 and ${x ∈ P_κλ| x ∩ κ$ is x-ineffable} has I-measure 1, where I is the complete ineffable ideal on $P_κλ$. As corollaries, we show that λ-ineffability does not imply complete λ-ineffability and that almost λ-ineffability does not imply λ-ineffability

Kategorie tematyczne

• 03E55: Large cardinals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994
• Tom: 145
• Numer: 2
• Strony: 141-151

Daty

wydano

1994

otrzymano

1993-03-10

poprawiono

1994-02-15

Twórcy

autor

Shizuo Kamo

• Department of Mathematics, University of Osaka, Prefecture Gakuen-chou, Sakai, Japan

Bibliografia

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• [4] D. Carr, $P_κλ$ partition relations, Fund. Math. 128 (1987), 181-195.
• [5] D. Carr and D. Pelletier, Towards a structure theory for ideals on $P_κλ$, in: Set Theory and its Applications, J. Steprāns and S. Watson (eds.), Lecture Notes in Math. 1401, Springer, 1987, 41-54.
• [6] T. Jech, Some combinatorial problems concerning uncountable cardinals, Ann. Math. Logic 5 (1973), 165-198.
• [7] C. A. Johnson, Distributive ideals and partition relations, J. Symbolic Logic 51 (1986), 617-625.
• [8] C. A. Johnson, Some partition relations for ideals on $P_κλ$, Acta Math. Hungar. 56 (1990), 269-282.