A note on sufficient conditions for no arbitrage

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Arbitrage and duality in nondominated discrete-time models (2013, background): “The second inequality corresponds to a version of the classical Superhedging Theorem with an additional weight function.”
THE RANGE OF TRADED OPTION PRICES (2007, background): “Laurent and Leisen (2000), Cousot (2004), and Buehler (2004) each make some attempt to describe how to choose a model from this class of consistent models.”
Arbitrage-free smoothing of the implied volatility surface (2009, background): “Hence the option call price quotes are free of static arbitrage (Carr et al. 2003, Carr and Madan 2005).”
Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints☆ (2015, unknown): “Remarkably, as it turns out, the sufficiency conditions also nicely embed as a special case recent theoretical results from Carr and Madan (2005) and Davis and Hobson (2007), which were obtained for linear option price surfaces.”
Arbitrage-free SVI volatility surfaces (2012, unknown): “Calendar spread arbitrage is usually expressed as the monotonicity of European call option prices with respect to the maturity (see for example [4] or [8]).”
Stochastic Local Volatility (2008, background): “The absence of dynamic arbitrage places constraints on the state probability space, and further complex conditions for absence of static arbitrage are required, as specified by Carr and Madan (2005) or Davis and Hobson (2007).”