: Results of a search for the electroweak associated production of charginos and next-to-lightest neutralinos, pairs of charginos or pairs of tau sleptons are presented. These processes are characterised by final states with at least two hadronically decaying tau leptons, missing transverse momentum and low jet activity. The analysis is based on an integrated luminosity of 20.3 fb−1 of proton-proton collisions at recorded with the ATLAS experiment at the Large Hadron Collider. No significant excess is observed with respect to the (...) predictions from Standard Model processes. Limits are set at 95% confidence level on the masses of the lighter chargino and next-to-lightest neutralino for various hypotheses for the lightest neutralino mass in simplified models. In the scenario of direct production of chargino pairs, with each chargino decaying into the lightest neutralino via an intermediate tau slepton, chargino masses up to 345 GeV are excluded for a massless lightest neutralino. For associated production of mass-degenerate charginos and next-to-lightest neutralinos, both decaying into the lightest neutralino via an intermediate tau slepton, masses up to 410 GeV are excluded for a massless lightest neutralino.[Figure not available: see fulltext.]. (shrink)
We isolate natural strengthenings of Bounded Martin’s Maximum which we call ${\mathsf{BMM}}^{*}$ and $A-{\mathsf{BMM}}^{*,++}$, and we investigate their consequences. We also show that if $A-{\mathsf{BMM}}^{*,++}$ holds true for every set of reals $A$ in $L$, then Woodin’s axiom $$ holds true. We conjecture that ${\mathsf{MM}}^{++}$ implies $A-{\mathsf{BMM}}^{*,++}$ for every $A$ which is universally Baire.
We show that L absoluteness for semi-proper forcings is equiconsistent with the existence of a remarkable cardinal, and hence by [6] with L absoluteness for proper forcings. By [7], L absoluteness for stationary set preserving forcings gives an inner model with a strong cardinal. By [3], the Bounded Semi-Proper Forcing Axiom is equiconsistent with the Bounded Proper Forcing Axiom , which in turn is equiconsistent with a reflecting cardinal. We show that Bounded Martin's Maximum is much stronger than BSPFA in (...) that if BMM holds, then for every X ∈ V , X# exists. (shrink)
We present several results relating the general theory of the stationary tower forcing developed by Woodin with forcing axioms. In particular we show that, in combination with class many Woodin cardinals, the forcing axiom MM++ makes the Π2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_2}$$\end{document}-fragment of the theory of Hℵ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H_{\aleph_2}}$$\end{document} invariant with respect to stationary set preserving forcings that preserve BMM. We argue that this is a promising generalization to (...) Hℵ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H_{\aleph_2}}$$\end{document} of Woodin’s absoluteness results for L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}$$\end{document}. In due course of proving this, we shall give a new proof of some of these results of Woodin. Finally we relate our generic absoluteness results with the resurrection axioms introduced by Hamkins and Johnstone and with their unbounded versions introduced by Tsaprounis. (shrink)
Several situations are presented in which there is an ordinal γ such that ${\{ X \in [\gamma]^{\aleph_0} : X \cap \omega_1 \in S\,{\rm and}\, ot(X) \in T \}}$ is a stationary subset of ${[\gamma]^{\aleph_0}}$ for all stationary ${S, T\subseteq \omega_1}$ . A natural strengthening of the existence of an ordinal γ for which the above conclusion holds lies, in terms of consistency strength, between the existence of the sharp of ${H_{\omega_2}}$ and the existence of sharps for all reals. Also, an (...) optimal model separating Bounded Semiproper Forcing Axiom (BSPFA) and Bounded Martin’s Maximum (BMM) is produced and it is shown that a strong form of BMM involving only parameters from ${H_{\omega_2}}$ implies that every function from ω 1 into ω 1 is bounded on a club by a canonical function. (shrink)
Several situations are presented in which there is an ordinal γ such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\{ X \in [\gamma]^{\aleph_0} : X \cap \omega_1 \in S\,{\rm and}\, ot \in T \}}$$\end{document} is a stationary subset of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${[\gamma]^{\aleph_0}}$$\end{document} for all stationary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S, T\subseteq \omega_1}$$\end{document}. A natural strengthening of the existence of an ordinal γ for which the above (...) conclusion holds lies, in terms of consistency strength, between the existence of the sharp of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H_{\omega_2}}$$\end{document} and the existence of sharps for all reals. Also, an optimal model separating Bounded Semiproper Forcing Axiom and Bounded Martin’s Maximum is produced and it is shown that a strong form of BMM involving only parameters from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H_{\omega_2}}$$\end{document} implies that every function from ω1 into ω1 is bounded on a club by a canonical function. (shrink)