Subcompact cardinals, squares, and stationary reflection

We generalise Jensen's result on the incompatibility of subcompactness with square. We show that alpha^+-subcompactness of some cardinal less than or equal to alpha precludes square_alpha, but also that square may be forced to hold everywhere where this obstruction is not present. The forcing also preserves other strong large cardinals. Similar results are also given for stationary reflection, with a corresponding strengthening of the large cardinal assumption involved. Finally, we refine the analysis by considering Schimmerling's hierarchy of weak squares, showing which cases are precluded by alpha^+-subcompactness, and again we demonstrate the optimality of our results by forcing the strongest possible squares under these restrictions to hold.Comment: 18 pages. Corrections and improvements from referee's report mad

Small u_kappa and large 2^kappa for supercompact kappa

In a recent preprint, Garti and Shelah state that the techniques of a paper of Dzamonja and Shelah can be used to force u_kappa to be kappa^+ for supercompact kappa with 2^kappa arbitrarily large. In this expository article we spell out the details of how this can be done.Comment: Expository article going through a specific application of the technique introduced in arXiv:math/0102043. 11 page

Indestructibility of Vopenka's Principle

We show that Vopenka's Principle and Vopenka cardinals are indestructible under reverse Easton forcing iterations of increasingly directed-closed partial orders, without the need for any preparatory forcing. As a consequence, we are able to prove the relative consistency of these large cardinal axioms with a variety of statements known to be independent of ZFC, such as the generalised continuum hypothesis, the existence of a definable well-order of the universe, and the existence of morasses at many cardinals.Comment: 15 pages, submitted to Israel Journal of Mathematic

Large cardinals and gap-1 morasses

We present a new partial order for directly forcing morasses to exist that enjoys a significant homogeneity property. We then use this forcing in a reverse Easton iteration to obtain an extension universe with morasses at every regular uncountable cardinal, while preserving all n-superstrong (0<n<omega+1), hyperstrong and 1-extendible cardinals. In the latter case, a preliminary forcing to make the GCH hold is required. Our forcing yields morasses that satisfy an extra property related to the homogeneity of the partial order; we refer to them as mangroves and prove that their existence is equivalent to the existence of morasses. Finally, we exhibit a partial order that forces universal morasses to exist at every regular uncountable cardinal, and use this to show that universal morasses are consistent with n-superstrong, hyperstrong, and 1-extendible cardinals. This all contributes to the second author's outer model programme, the aim of which is to show that L-like principles can hold in outer models which nevertheless contain large cardinals.Comment: 49 page

Inhabitants of interesting subsets of the Bousfield lattice

In 1979, Bousfield defined an equivalence relation on the stable homotopy category. The set of Bousfield classes has some important subsets such as the distributive lattice DL of all classes 〈E〉which are smash idempotent and the complete Boolean algebra cBA of closed classes. We provide examples of spectra that are in DL, but not in cBA; in particular, for every prime p, the Bousfield class of the Eilenberg–MacLane spectrum 〈HFp〉 is in DL∖cBA

Utilisation of an operative difficulty grading scale for laparoscopic cholecystectomy

Background A reliable system for grading operative difficulty of laparoscopic cholecystectomy would standardise description of findings and reporting of outcomes. The aim of this study was to validate a difficulty grading system (Nassar scale), testing its applicability and consistency in two large prospective datasets. Methods Patient and disease-related variables and 30-day outcomes were identified in two prospective cholecystectomy databases: the multi-centre prospective cohort of 8820 patients from the recent CholeS Study and the single-surgeon series containing 4089 patients. Operative data and patient outcomes were correlated with Nassar operative difficultly scale, using Kendall’s tau for dichotomous variables, or Jonckheere–Terpstra tests for continuous variables. A ROC curve analysis was performed, to quantify the predictive accuracy of the scale for each outcome, with continuous outcomes dichotomised, prior to analysis. Results A higher operative difficulty grade was consistently associated with worse outcomes for the patients in both the reference and CholeS cohorts. The median length of stay increased from 0 to 4 days, and the 30-day complication rate from 7.6 to 24.4% as the difficulty grade increased from 1 to 4/5 (both p < 0.001). In the CholeS cohort, a higher difficulty grade was found to be most strongly associated with conversion to open and 30-day mortality (AUROC = 0.903, 0.822, respectively). On multivariable analysis, the Nassar operative difficultly scale was found to be a significant independent predictor of operative duration, conversion to open surgery, 30-day complications and 30-day reintervention (all p < 0.001). Conclusion We have shown that an operative difficulty scale can standardise the description of operative findings by multiple grades of surgeons to facilitate audit, training assessment and research. It provides a tool for reporting operative findings, disease severity and technical difficulty and can be utilised in future research to reliably compare outcomes according to case mix and intra-operative difficulty

Targeting DNA Damage Response and Replication Stress in Pancreatic Cancer

Background and aims: Continuing recalcitrance to therapy cements pancreatic cancer (PC) as the most lethal malignancy, which is set to become the second leading cause of cancer death in our society. The study aim was to investigate the association between DNA damage response (DDR), replication stress and novel therapeutic response in PC to develop a biomarker driven therapeutic strategy targeting DDR and replication stress in PC. Methods: We interrogated the transcriptome, genome, proteome and functional characteristics of 61 novel PC patient-derived cell lines to define novel therapeutic strategies targeting DDR and replication stress. Validation was done in patient derived xenografts and human PC organoids. Results: Patient-derived cell lines faithfully recapitulate the epithelial component of pancreatic tumors including previously described molecular subtypes. Biomarkers of DDR deficiency, including a novel signature of homologous recombination deficiency, co-segregates with response to platinum (P &lt; 0.001) and PARP inhibitor therapy (P &lt; 0.001) in vitro and in vivo. We generated a novel signature of replication stress with which predicts response to ATR (P &lt; 0.018) and WEE1 inhibitor (P &lt; 0.029) treatment in both cell lines and human PC organoids. Replication stress was enriched in the squamous subtype of PC (P &lt; 0.001) but not associated with DDR deficiency. Conclusions: Replication stress and DDR deficiency are independent of each other, creating opportunities for therapy in DDR proficient PC, and post-platinum therapy