We investigate the effects of various forcings on several forms of the Halpern-Läuchli Theorem. For inaccessible κ, we show they are preserved by forcings of size less than κ. Combining this with work of Zhang in [17] yields that the polarized partition relations associated with finite products of the κ-rationals are preserved by all forcings of size less than κ over models satisfying the Halpern-Läuchli Theorem at κ. We also show that the Halpern-Läuchli Theorem is preserved by <κ-closed forcings assuming κ is measurable, following some observed reflection properties.

The Atacama Desert, the driest and oldest desert in the world, is a hostile environment for life. Despite the inhospitable conditions, bacterial sequences detected in this location suggest rich bacterial life. This study tested the idea that certain bacteria would thrive in this location and that some of them could be cultivated permitting further characterization. Environmental surface soil samples from 1-5 cm deep were collected from 18 diverse locations within the Atacama Desert. To assess the bacterial taxa, diversity, and abundance, Illumina 16S rRNA gene sequencing was performed directly on soil samples. Bacteria were also cultured from the samples. We have a collection of 74 unique bacterial isolates after cultivation and confirmation by 16S rRNA gene sequencing. Pigmentation, biofilm formation, antibiotic production against Escherichia coli MG1655 and Staphylococcus aureus HG003, and antibiotic resistance were assessed on these isolates. We found that approximately a third of the colonies produced pigments, 80% of isolates formed biofilms, many isolates had antibiotic activity against E. coli and/or S. aureus, and many were resistant to commercial antibiotics. The functional characterization of these isolates gives us insight into the adaptive bacterial strategies in harsh environments and enables us to learn about their possible use in agriculture, healthcare, or biotechnology.Originality-Significant StatementThis study provides the first microbial diversity analysis from Atacama Desert soil, presents the cultivation and isolation of 74 unique bacterial isolates, many of which may be novel genera and species, and explores pigment production, antibiotic production and resistance, and unique biofilm development as bacterial survival strategies for living within extreme environments.

Henle, Mathias, and Woodin proved in [21] that, provided that holds in a model M of ZF, then forcing with over M adds no new sets of ordinals, thus earning the name a “barren” extension. Moreover, under an additional assumption, they proved that this generic extension preserves all strong partition cardinals. This forcing thus produces a model , where is a Ramsey ultrafilter, with many properties of the original model M. This begged the question of how important the Ramseyness of is for these results. In this paper, we show that several classes of -closed forcings which generate non-Ramsey ultrafilters have the same properties. Such ultrafilters include Milliken–Taylor ultrafilters, a class of rapid p-points of Laflamme, k-arrow p-points of Baumgartner and Taylor, and extensions to a class of ultrafilters constructed by Dobrinen, Mijares, and Trujillo. Furthermore, the class of Boolean algebras , , forcing non-p-points also produce barren extensions.