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- W2634783606 abstract "We investigate the effects of various forcings on several forms of the Halpern-Lauchli Theorem. For inaccessible $kappa$, we show they are preserved by forcings of size less than $kappa$. Combining this with work of Zhang in cite{Zhang17} yields that the polarized partition relations associated with finite products of the $kappa$-rationals are preserved by all forcings of size less than $kappa$ over models satisfying the Halpern-Lauchli Theorem at $kappa$. We also show that the Halpern-Lauchli Theorem is preserved by ${{<}kappa}$-closed forcings assuming $kappa$ is measurable, following some observed reflection properties." @default.
- W2634783606 created "2017-06-30" @default.
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- W2634783606 date "2017-06-25" @default.
- W2634783606 modified "2023-09-23" @default.
- W2634783606 title "Forcing and the Halpern-Lauchli Theorem" @default.
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- W2634783606 doi "https://doi.org/10.48550/arxiv.1706.08174" @default.
- W2634783606 hasPublicationYear "2017" @default.
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