Zilber's Quasiminimality Conjecture states that the complex field equipped with the exponential function is quasiminimal, i.e. every definable subset is countable or co-countable. Despite remaining open, this conjecture led to multiple new concepts and results. One of the directions inspired by the conjecture is the investigation of analogous conjectures where the exponential map is replaced with another function or a function-like object. In most cases the obtained conjecture seems to stay as difficult as the exponential one; as pointed out by Koiran and Wilkie, it even remains open whether adding all entire functions to the complex field would make it quasiminimal or non-quasiminimal. In this talk we provide two quasiminimal examples of this sort: first one involves a correspondence between two elliptic curves, while the second one considers the theory of a generic function, as introduced by Zilber in 2002.
Zilber's Quasiminimality Conjecture states that the complex field equipped with the exponential function is quasiminimal, i.e. every definable subset is countable or co-countable. Despite remaining open, this conjecture led to multiple new concepts and results. One of the directions inspired by the conjecture is the investigation of analogous conjectures where the exponential map is replaced with another function or a function-like object. In most cases the obtained conjecture seems to stay as difficult as the exponential one; as pointed out by Koiran and Wilkie, it even remains open whether adding all entire functions to the complex field would make it quasiminimal or non-quasiminimal. In this talk we provide two quasiminimal examples of this sort: first one involves a correspondence between two elliptic curves, while the second one considers the theory of a generic function, as introduced by Zilber in 2002.
There was another possible development: Reuters also reported that Ukraine said that Belarus could soon join the invasion of Ukraine. However, the AFP, citing a Pentagon official, said the U.S. hasn’t yet seen evidence that Belarusian troops are in Ukraine. In addition, Telegram now supports the use of third-party streaming tools like OBS Studio and XSplit to broadcast live video, allowing users to add overlays and multi-screen layouts for a more professional look. The perpetrators use various names to carry out the investment scams. They may also impersonate or clone licensed capital market intermediaries by using the names, logos, credentials, websites and other details of the legitimate entities to promote the illegal schemes. Apparently upbeat developments in Russia's discussions with Ukraine helped at least temporarily send investors back into risk assets. Russian President Vladimir Putin said during a meeting with his Belarusian counterpart Alexander Lukashenko that there were "certain positive developments" occurring in the talks with Ukraine, according to a transcript of their meeting. Putin added that discussions were happening "almost on a daily basis." One thing that Telegram now offers to all users is the ability to “disappear” messages or set remote deletion deadlines. That enables users to have much more control over how long people can access what you’re sending them. Given that Russian law enforcement officials are reportedly (via Insider) stopping people in the street and demanding to read their text messages, this could be vital to protect individuals from reprisals.
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