10.23638/LMCS-13(3:16)2017
https://lmcs.episciences.org/3659
Kudinov, Oleg
Oleg
Kudinov
Selivanov, Victor
Victor
Selivanov
First Order Theories of Some Lattices of Open Sets
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.
episciences.org
Mathematics - Logic
Computer Science - Logic in Computer Science
03D78, 03D45, 03D55, 03D30
arXiv.org - Non-exclusive license to distribute
2017-08-25
2017-08-25
2017-08-25
eng
journal article
arXiv:1705.04564
10.48550/arXiv.1705.04564
1860-5974
https://lmcs.episciences.org/3659/pdf
VoR
application/pdf
Logical Methods in Computer Science
Volume 13, Issue 3
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