Видеотека: С. О. Сперанский, Monadic second-order definability in weak arithmetics

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Конференция международных математических центров мирового уровня 10 августа 2021 г. 15:20, г. Сочи

Monadic second-order definability in weak arithmetics С. О. Сперанский Математический институт им. В.А. Стеклова Российской академии наук, г. Москва
Аннотация: I shall give a survey of monadic second-order definability in relatively weak arithmetical structures on $\mathbb{N}$, such as $$ \langle \mathbb{N}; \leqslant \rangle , \quad \langle \mathbb{N}; +, = \rangle , \quad \langle \mathbb{N}; \,\| \,\rangle , \quad \langle \mathbb{N}; \bot \rangle \quad \text{and} \quad \langle \mathbb{N}; \times, = \rangle $$ where $\|$ and $\bot$ denote the divisibility relation and the coprimeness relation respectively. Moreover, if time permits, I shall mention some related results on first-order definability. The topic of this talk may be described as ‘weak arithmetics’, broadly understood.