The article considers the ontological significance of the objective phenomenology of Alain Badiou, as it is presented in his works «Logic of worlds» and «Second manifesto for philosophy». The author compares Badiou’s phenomenology with the phenomenological projects of Husserl and Heidegger, noting its subject less character. The dissolution of the ontological subject in related reaction to the events by diverse strategies implemented in the subjectivity is performed in the objective phenomenology of Badiou by eliminating of the instance of contemplation in favor of ethical and political practice. Special attention is paid to the relationship of ontology and mathematics, as well as to the analysis of the concepts of the subject and post-eventuality in the context of traditional ontological categories of the one and the multiple. The conclusion is that in the modern ontological theory of the transition from the analysis of isolated nature of the phenomenon to the analysis of a single set–much.