Наредни састанак Семинара биће одржан у петак, 20. октобра 2023, у сали 301ф Математичког института САНУ са почетком у 16.15. У питању је заједнички састанак семинара са Одељењем за матекатику.
Предавач: Станислав Сперански, Steklov Mathematical Institute, Moscow
Наслов предавања: ELEMENTARY THEORIES OF CLASSES OF PROBABILITY SPACES
Апстракт: We shall be concerned with a two-sorted probabilistic language, denoted by QPL, which contains quantifiers over events and over reals. It is obtained by combining the elementary language of Boolean algebras and that of ordered fields in a natural way, and can be viewed as an elementary language for reasoning about probability spaces. The fragment of QPL containing only quantifiers over reals (but not over events) is a variant of the well-known `polynomial’ probability logic from [Fagin, Halpern, Megiddo 1990: Section 6]. First we prove that the QPL-theory of the Lebesgue measure on [0, 1] is decidable, and moreover, all atomless spaces have the same QPL-theory. Then we introduce the notion of elementary invariant for QPL, and use it to translate the semantics for QPL into the setting of elementary analysis. This allows us to obtain further decidability results as well as to provide exact complexity upper bounds for a range of interesting undecidable theories.
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