eng
episciences.org
Logical Methods in Computer Science
1860-5974
2017-08-25
Volume 13, Issue 3
10.23638/LMCS-13(3:16)2017
3659
journal article
First Order Theories of Some Lattices of Open Sets
Oleg Kudinov
Victor Selivanov
We show that the first order theory of the lattice of open sets in some
natural topological spaces is $m$-equivalent to second order arithmetic. We
also show that for many natural computable metric spaces and computable domains
the first order theory of the lattice of effectively open sets is undecidable.
Moreover, for several important spaces (e.g., $\mathbb{R}^n$, $n\geq1$, and the
domain $P\omega$) this theory is $m$-equivalent to first order arithmetic.
https://lmcs.episciences.org/3659/pdf
Mathematics - Logic
Computer Science - Logic in Computer Science
03D78, 03D45, 03D55, 03D30