Wider Thin-Very Tall Superatomic Boolean Algebras

For each regular cardinal k > w we show the consistent existence of a thin very tall superatomic Boolean algebra of width k.Comment: There is a gap in claim 4.

Combinatorial Properties and Dependent choice in symmetric extensions based on L\'{e}vy Collapse

We work with symmetric extensions based on L\'{e}vy Collapse and extend a few results of Arthur Apter. We prove a conjecture of Ioanna Dimitriou from her P.h.d. thesis. We also observe that if $V$ is a model of ZFC, then $DC_{<\kappa}$ can be preserved in the symmetric extension of $V$ in terms of symmetric system $\langle \mathbb{P},\mathcal{G},\mathcal{F}\rangle$, if $\mathbb{P}$ is $\kappa$-distributive and $\mathcal{F}$ is $\kappa$-complete. Further we observe that if $V$ is a model of ZF + $DC_{\kappa}$, then $DC_{<\kappa}$ can be preserved in the symmetric extension of $V$ in terms of symmetric system $\langle \mathbb{P},\mathcal{G},\mathcal{F}\rangle$, if $\mathbb{P}$ is $\kappa$-strategically closed and $\mathcal{F}$ is $\kappa$-complete.Comment: Revised versio

Strong coding

AbstractWe present here a refinement of the method of Jensen coding [7] and apply it to the study of admissible ordinals. An ordinal α is recursively inaccessible if it is both admissible and the limit of admissible ordinals. Solovay asked if it is consistent to have a real R such that the R-admissible ordinals equal the recursively inaccessible ordinals. This is a problem in class forcing as any real in a set generic extension of L must preserve the admissibility of a final segment of the admissible ordinals.Our main theorem provides an affirmative solution to Solovay's problem

Proxy records of paleohurricanes for the western and southern caribbean

This dissertation evaluates the hypothesis that hurricane activity levels in the North Atlantic during the late Holocene have been driven by latitudinal movements of the North Atlantic circulation system. Multi-millennial sedimentary proxy records, based on the occurrence of overwash clastic layers, provide clear evidence of abruptly alternating periods of hurricane landfall frequency for Nicaragua and Belize. Three Belizean transects exhibit an Active period (hyperactivity) occurring from ~2000-6000 cal yr BP, although dating is inconsistent across the transects. An Active period covering the last 500 years is found at one location. The Nicaraguan record, derived from three transects covering \u3e90 km of coastline, consistently displays an Active period covering the last 800 years, preceded by a Quiet period that lasts until at least ~2800 years BP, before which time environmental factors render the sites insensitive. For both coastlines the calculated strike frequency increased by a factor of 3-12 during Active periods. The Barbados depositional record is characterized by sudden shifts from organic to clay, attributed to increased aridity, with the arid periods being roughly contemporaneous with the Active periods occurring in Belize and Nicaragua, as well as periods of southern residency of the Intertropical Convergence Zone. Latitudinal movements of a unified North Atlantic circulation system were probably the driver of these changes, with southern migration increasing both landfall frequency and aridity regionally. When correlated with published records, the timing of activity regime changes identified from our sites indicates that periods of increased hurricane activity proceed across the North Atlantic in a time-transgressive manner, with the Caribbean hyperactive period preceding that of the Gulf of Mexico. The Active period for Nicaragua beginning ~850 years BP is anti-phase with a recently published model, predicated upon basin-wide synchroneity in activity patterns. This discrepancy possibly results from differences in spatial coverage, as correlations between hurricane landfall and track patterns indicate three distinct groupings resulting from atmospheric conditions. The basin-wide pattern is derived from locations contained within a single (Atlantic coast) track set, while our time-transgressive model is derived from sites within both the Caribbean and Gulf of Mexico track sets