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Steklov Mathematical Institute Seminar
January 22, 2015 16:00, Moscow, Steklov Mathematical Institute of RAS, Conference Hall (8 Gubkina)
 


Positive logic for reflection principles in arithmetic

L. D. Beklemishev
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L. D. Beklemishev
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Abstract: Reflection principles in arithmetic are well-known generalizations of Gödel's sentence expressing the consistency of a given arithmetical theory. Similarly to Gödel's sentence, they yield stronger examples of independent arithmetical statements. From a more general point of view, these schemata can be considered as operations on arithmetical theories. The main result of this talk gives, in a sense, an exhaustive description of algebraic properties of these operations. Connections of these area with modal logic and Kripke models will be discussed.
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