On a convenient property about [γ]

D. Asperó

doi:10.1007/s00153-009-0142-6

On a convenient property about [γ]

D. Asperó

Logic

Research output: Contribution to journal › Article › peer-review

Abstract

Several situations are presented in which there is an ordinal ? such that is a stationary subset of for all stationary subset of [?] for all stationary S,T ??. A natural strengthening of the existence of an ordinal ? for which the above conclusion holds lies, in terms of consistency strength, between the existence of the sharp of and the existence of sharps for all reals. Also, an optimal model separating Bounded Semiproper Forcing Axiom (BSPFA) and Bounded Martin's Maximum (BMM) is produced and it is shown that a strong form of BMM involving only parameters from Himplies that every function from ? into ? is bounded on a club by a canonical function.

Original language	English
Pages (from-to)	653-677
Number of pages	25
Journal	Archive for Mathematical Logic
Volume	48
Issue number	7
DOIs	https://doi.org/10.1007/s00153-009-0142-6
Publication status	Published - 1 Sep 2009

Keywords

03E05
03E57
03E55
03E35

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10.1007/s00153-009-0142-6

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AB - Several situations are presented in which there is an ordinal ? such that is a stationary subset of for all stationary subset of [?] for all stationary S,T ??. A natural strengthening of the existence of an ordinal ? for which the above conclusion holds lies, in terms of consistency strength, between the existence of the sharp of and the existence of sharps for all reals. Also, an optimal model separating Bounded Semiproper Forcing Axiom (BSPFA) and Bounded Martin's Maximum (BMM) is produced and it is shown that a strong form of BMM involving only parameters from Himplies that every function from ? into ? is bounded on a club by a canonical function.

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KW - 03E35

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SN - 0933-5846

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ER -

On a convenient property about [γ]

Abstract

Keywords

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