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We show that the Abraham–Rubin–Shelah Open Coloring Axiom is consistent with a large continuum, in particular, consistent with [Formula: see text]. This answers one of the main open questions from [U. Abraham, M. Rubin and S. Shelah, On the consistency of some partition theorems for continuous colorings, and the structure of [Formula: see text]-dense real order types, Ann. Pure Appl. Logic 325(29) (1985) 123–206]. As in [U. Abraham, M. Rubin and S. Shelah, On the consistency of some partition theorems for continuous colorings, and the structure of [Formula: see text]-dense real order types, Ann. Pure Appl. Logic 325(29) (1985) 123–206], we need to construct names for the so-called preassignments of colors in order to add the necessary homogeneous sets. However, the known constructions of preassignments (ours in particular) only work assuming the [Formula: see text]. In order to address this difficulty, we show how to construct such names with very strong symmetry conditions. This symmetry allows us to combine them in many different ways, using a new type of poset called a partition product. Partition products may be thought of as a restricted memory iteration with stringent isomorphism and coherent-overlap conditions on the memories. We finally construct, in [Formula: see text], the partition product which gives us a model of [Formula: see text] in which [Formula: see text].
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The partition of organic compounds from water into the methyl isobutyl ketone extraction solvent with updated Abraham model equation
Experimental water-to-methyl isobutyl ketone partition coefficientshave been determined for 27 different organic solutes based on gaschromatographic measurements. Updated Abraham model correlationswere determined for describing solute transfer into methyl isobutylketone by combining the measured partition coefficient data deter-mined in the present study with published experimental values takenfrom chemical and engineering literature. One hundred nineteen com-pounds were used in determining the revised Abraham model correla-tions. After calculations, the revised mathematical correlations werefound to match the experimental data to within an overall averagestandard deviation of 0.21 log units.
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- Award ID(s):
- 1757946
- PAR ID:
- 10188203
- Publisher / Repository:
- Taylor & Francis
- Date Published:
- Journal Name:
- Physics and Chemistry of Liquids
- Volume:
- 59
- Issue:
- 3
- ISSN:
- 0031-9104
- Page Range / eLocation ID:
- 431-441
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1080/00319104.2020.1732375
