Vladislav Amstislavskiy: On the elementary theories of lattices of continuous functions; Svetlana Aleksandrova: On ∑-definability
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On the elementary theories of lattices of continuous functions
Vladislav Amstislavskiy
A. P. Ershov Institute of Informatics Systems
Novosibirsk, Rusija
Abstract: The topic mostly concerns decidability problem of the elementary theories of continuous functions over reals. It is proved that the theory of C(R) (continuous functions from R to R) with pointwise order is decidable. Then, it is demonstrated that the theories of continuous functions and open sets are m-equivalent for quite a wide class of spaces. To prove these facts we used classical methods and also the new generalized method of interpretations that was offered by Oleg Kudinov.
On ∑-definability
Svetlana Aleksandrova
A. P. Ershov Institute of Informatics Systems
Novosibirsk, Rusija
