A model of the ontology of time

[Update Jun 2026. For the current form of the project see Philpapers CLBMOV] In this paper I give minimal axioms for the ontology of time, especially A-theories and B-theories and I derive philosophically interesting lemmas. The exercise is set-theoretical, defining all notions and indicating assumptions and philosophical points of disagreement, while being easy to translate to other formal expressions. The issue of a logic for A-theories of time is treated towards the end, where I sketch ‘copresent’ operators for capturing the idea of temporal passage. The main conclusion will be that, while circularity threatens both families of theories, the growing block theory (belonging to the A-theory) is the least objectionable philosophically.