3,215 research outputs found
The complexity of classification problems for models of arithmetic
We observe that the classification problem for countable models of arithmetic
is Borel complete. On the other hand, the classification problems for finitely
generated models of arithmetic and for recursively saturated models of
arithmetic are Borel; we investigate the precise complexity of each of these.
Finally, we show that the classification problem for pairs of recursively
saturated models and for automorphisms of a fixed recursively saturated model
are Borel complete.Comment: 15 page
Modal logic S4 as a paraconsistent logic with a topological semantics
In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new proof of S4 as being "the logic of topological spaces", but now under the perspective of paraconsistency
Ample Pairs
We show that the ample degree of a stable theory with trivial forking is
preserved when we consider the corresponding theory of belles paires, if it
exists. This result also applies to the theory of -structures of a trivial
theory of rank .Comment: Research partially supported by the program MTM2014-59178-P. The
second author conducted research with support of the programme
ANR-13-BS01-0006 Valcomo. The third author would like to thank the European
Research Council grant 33882
Ample Pairs
We show that the ample degree of a stable theory with trivial forking is
preserved when we consider the corresponding theory of belles paires, if it
exists. This result also applies to the theory of -structures of a trivial
theory of rank .Comment: Research partially supported by the program MTM2014-59178-P. The
second author conducted research with support of the programme
ANR-13-BS01-0006 Valcomo. The third author would like to thank the European
Research Council grant 33882
Actions on permutations and unimodality of descent polynomials
We study a group action on permutations due to Foata and Strehl and use it to
prove that the descent generating polynomial of certain sets of permutations
has a nonnegative expansion in the basis ,
. This property implies symmetry and unimodality. We
prove that the action is invariant under stack-sorting which strengthens recent
unimodality results of B\'ona. We prove that the generalized permutation
patterns and are invariant under the action and use this to
prove unimodality properties for a -analog of the Eulerian numbers recently
studied by Corteel, Postnikov, Steingr\'{\i}msson and Williams.
We also extend the action to linear extensions of sign-graded posets to give
a new proof of the unimodality of the -Eulerian polynomials of
sign-graded posets and a combinatorial interpretations (in terms of
Stembridge's peak polynomials) of the corresponding coefficients when expanded
in the above basis.
Finally, we prove that the statistic defined as the number of vertices of
even height in the unordered decreasing tree of a permutation has the same
distribution as the number of descents on any set of permutations invariant
under the action. When restricted to the set of stack-sortable permutations we
recover a result of Kreweras.Comment: 19 pages, revised version to appear in Europ. J. Combi
- …