PFA(S)[S]: more mutually consistent topological consequences of PFA and V = L
نویسنده
چکیده
Extending work of [14, 16, 26], we show there is a model of set theory in which normal spaces are collectionwise Hausdorff if they are either first countable or locally compact, and yet there are no first countable L-spaces or compact S-spaces. The model is one of the form PFA(S)[S], where S is a coherent Souslin tree.
منابع مشابه
A Useful Model ( Notes for 2011 Summer Topology Conference )
In these notes and the accompanying lectures I introduce models of form PFA(S)[S], a useful class of models of set theory in which various consequences of both PFA and V = L hold. We list some of these consequences and topologically derive new results from them. Then we present some of the characteristic set-theoretic methods used to prove things in these models.
متن کاملPfa(s) and Countable Tightness
Todorcevic introduced the forcing axiom PFA(S) and established many consequences. We contribute to this project. In particular, we consider status under PFA(S) of two important consequences of PFA concerning spaces of countable tightness. In particular we prove that the existence of a Souslin tree does not imply the existence of a compact non-sequential space of countable tightness. We contrast...
متن کاملThe Present Situation of Patellofemoral Arthroplasty in the Management of Solitary Patellofemoral Osteoarthritis
Patellofemoral (PF) osteoarthritis (OA) is a somewhat predominant illness, affecting up to 24% of women and 11% ofmen over the age of 55 years who suffer from symptomatic knee OA. The purposes of this narrative overview are tosummarize the present situation of patellofemoral arthroplasty (PFA) in the treatment of solitary PF-OA, and to givean account of the clinical results of...
متن کاملCartan's topological structure
A system of di®erential forms will establish a topology and a topological structure on a domain of independent variables such that is possible to determine which maps or processes acting on the system are continuous. Perhaps the most simple topology is that generated by the existence of a single 1-form of Action, its Pfa® sequence of exterior di®erentials, and their intersections. In such a top...
متن کاملGlyoxal as an alternative fixative to formaldehyde in immunostaining and super‐resolution microscopy
Paraformaldehyde (PFA) is the most commonly used fixative for immunostaining of cells, but has been associated with various problems, ranging from loss of antigenicity to changes in morphology during fixation. We show here that the small dialdehyde glyoxal can successfully replace PFA Despite being less toxic than PFA, and, as most aldehydes, likely usable as a fixative, glyoxal has not yet bee...
متن کامل