Nonproper products

Roslanowski, Andrzej; Shelah, Saharon; Spinas, Otmar

doi:10.1112/blms/bdr094

Cited by 5 publications

(4 citation statements)

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“…A minimum spanning tree was generated using Phyloviz (v2.0) and the therein implemented goeBURST algorithm 59 . We used a 5, 12 and 25 SNPs cut-off to delineate genomic clusters 60 among the core SNP alignment using R along with the ape package and the hclust function. The patient address was plotted in a map using the online tool Microreact ( www.microreact.org ).…”

Section: Methodsmentioning

confidence: 99%

Genomic epidemiology of Mycobacterium tuberculosis in Santa Catarina, Southern Brazil

Verza

Scheffer

Salvato

et al. 2020

Sci Rep

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Mycobacterium tuberculosis (M.tb), the pathogen responsible for tuberculosis (TB) poses as the major cause of death among infectious diseases. The knowledge about the molecular diversity of M.tb enables the implementation of more effective surveillance and control measures and, nowadays, Whole Genome Sequencing (WGS) holds the potential to produce high-resolution epidemiological data in a high-throughput manner. Florianópolis, the state capital of Santa Catarina (SC) in south Brazil, shows a high TB incidence (46.0/100,000). Here we carried out a WGS-based evaluation of the M.tb strain diversity, drug-resistance and ongoing transmission in the capital metropolitan region. Resistance to isoniazid, rifampicin, streptomycin was identified respectively in 4.0% (n = 6), 2.0% (n = 3) and 1.3% (n = 2) of the 151 studied strains by WGS. Besides, resistance to pyrazinamide and ethambutol was detected in 0.7% (n = 1) and reistance to ethionamide and fluoroquinolone (FQ) in 1.3% (n = 2), while a single (0.7%) multidrug-resistant (MDR) strain was identified. SNP-based typing classified all isolates into M.tb Lineage 4, with high proportion of sublineages LAM (60.3%), T (16.4%) and Haarlem (7.9%). The average core-genome distance between isolates was 420.3 SNPs, with 43.7% of all isolates grouped across 22 genomic clusters thereby showing the presence of important ongoing TB transmission events. Most clusters were geographically distributed across the study setting which highlights the need for an urgent interruption of these large transmission chains. The data conveyed by this study shows the presence of important and uncontrolled TB transmission in the metropolitan area and provides precise data to support TB control measures in this region.

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Section: Methodsmentioning

confidence: 99%

Genomic epidemiology of Mycobacterium tuberculosis in Santa Catarina, Southern Brazil

Verza

Scheffer

Salvato

et al. 2020

Sci Rep

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“…We note that F = { F * * ,g : g ∈ G } ≥ Since α 1 = α 2 are in u \ w we may apply Lemma 5.3 (2) to get that nor 0 i (F 1 * F 2 ) = 0, contradicting ( * ) 7 . Thus, putting together ( * ) 3 and ( * ) 6 + ( * ) 8 we conclude that ( * ) 9 if h ∈ set(F 1 * F 2 ),x ∈ S u,i andȳ = sucx (h), η = H (ȳ u ) (for = 1, 2), then η 1 = η 2 ⇒ (g yi (α 1 ) −1 • f yi (α 1 ))(η 1 ) = (g yi (α 2 ) −1 • f yi (α 2 ))(η 2 ).…”

Section: Lemma 51mentioning

confidence: 98%

“…[Why is this possible? We can choose them to satisfy clause (a) by ( * ) 8 and clauses (b) and (c) follow: look at the choices inside ( * ) 7 .] Now we stop fixing g ∈ G. Put G 1 = {g ∈ G : ι g = 1 and m 1,g = m 2,g } and G 2 = {g ∈ G : ι g = 1 or m 1,g = m 2,g }.…”

Section: Lemma 51mentioning

confidence: 99%

Models of expansions of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb N}$\end{document} with no end extensions

Shelah

2011

Mathematical Logic Quarterly

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Key words Models of Peano arithmetic, end extensions, forcing with creatures. MSC (2010) 03C62, 03E35, 03E40We deal with models of Peano arithmetic (specifically with a question of Ali Enayat). The methods are from creature forcing. We find an expansion of N such that its theory has models with no (elementary) end extensions. In fact there is a Borel uncountable set of subsets of N such that expanding N by any uncountably many of them suffice. Also we find arithmetically closed A with no ultrafilter on it with suitable definability demand (related to being Ramsey).

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“…Such is the case with many forcing arguments. For instance, the proofs of propernes of some forcing notions built according to the scheme of norms on possibilities have in their hearts partition theorems stating that at some situations a homogeneous tree and/or a sequence of creatures determining a condition can be found (see, e.g., Ros lanowski and Shelah [7,8], Ros lanowski, Shelah and Spinas [9], Kellner and Shelah [6,5]). A more explicit connection of partition theorems with forcing arguments is given in Shelah and Zapletal [10].…”

Section: Introductionmentioning

confidence: 99%

Partition Theorems from Creatures and Idempotent Ultrafilters

Roslanowski

Shelah

2013

Ann. Comb.

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Abstract. We show a general scheme of Ramsey-type results for partitions of countable sets of finite functions, where "one piece is big" is interpreted in the language originating in creature forcing. The heart of our proofs follows Glazer's proof of the Hindman Theorem, so we prove the existence of idempotent ultrafilters with respect to suitable operation. Then we deduce partition theorems related to creature forcings. IntroductionA typical partition theorem asserts that if a set with some structure is divided into some number of "nice" pieces, then one of the pieces is large from the point of the structure under considerations. Sometimes, the underlying structure is complicated and it is not immediately visible that the arguments in hands involve a partition theorem. Such is the case with many forcing arguments. For instance, the proofs of propernes of some forcing notions built according to the scheme of norms on possibilities have in their hearts partition theorems stating that at some situations a homogeneous tree and/or a sequence of creatures determining a condition can be found (see, e.g., Ros lanowski and Shelah [7,8], Ros lanowski, Shelah and Spinas [9], Kellner and Shelah [6,5]). A more explicit connection of partition theorems with forcing arguments is given in Shelah and Zapletal [10].The present paper is a contribution to the Ramsey theory in the context of finitary creature forcing. We are motivated by earlier papers and notions concerning norms on possibilities, but we do not look at possible forcing consequences. The common form of our results here is as follows. If a certain family of partial finite functions is divided into finitely many pieces, then one of the pieces contains all partial functions determined by an object ("a pure candidate") that can be interpreted as a forcing condition if we look at the setting from the point of view of the creature forcing. Sets of partial functions determined by a pure candidate might be considered as "large" sets.Our main proofs are following the celebrated Glazer's proof of the Hindman Theorem, which reduced the problem to the existence of a relevant ultrafilter on ω in ZFC. Those arguments were presented by Comfort in [2, Theorem 10.3, p.451] with [2, Lemma 10.1, p.449] as a crucial step (stated here in 2.7). The arguments of the second section of our paper really resemble Glazer's proof. In that section we deal with the easier case of omittory-like creatures (loose FFCC pairs of 1.2(2))

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Nonproper products

Abstract: We show that there exist two proper creature forcings having a simple (Borel) definition, whose product is not proper. We also give a new condition ensuring properness of some forcings with norms.

Cited by 5 publications

References 5 publications

Genomic epidemiology of Mycobacterium tuberculosis in Santa Catarina, Southern Brazil

Genomic epidemiology of Mycobacterium tuberculosis in Santa Catarina, Southern Brazil

Models of expansions of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb N}$\end{document} with no end extensions

Partition Theorems from Creatures and Idempotent Ultrafilters

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