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We say that a cardinal function \({\phi}\) reflects an infinite cardinal \({\kappa}\), if given a topological space X with \({\phi(X) \geqq \kappa}\), there exists \({Y \in [X]^{\leqq \kappa}}\) with \({\phi(Y ) \geqq \kappa}\). We improve results of Hodel and Vaughan in [8], investigating under what conditions the cardinal function L (Lindelof degree) reflects an inaccessible cardinal. We show that L reflects all strongly inaccessible cardinals, and obtain several sufficient conditions under which L reflects a weakly inaccessible cardinal. We discuss some combinatorial principles relevant to the problem, like SSH (Shelah’s Strong Hypothesis) and SWH (Shelah’s Weak Hypothesis), and show that if \({0^\sharp}\) does not exist, then L reflects all weakly inaccessible cardinals.