1,194 research outputs found
Linear extensions of partial orders and Reverse Mathematics
We introduce the notion of \tau-like partial order, where \tau is one of the
linear order types \omega, \omega*, \omega+\omega*, and \zeta. For example,
being \omega-like means that every element has finitely many predecessors,
while being \zeta-like means that every interval is finite. We consider
statements of the form "any \tau-like partial order has a \tau-like linear
extension" and "any \tau-like partial order is embeddable into \tau" (when
\tau\ is \zeta\ this result appears to be new). Working in the framework of
reverse mathematics, we show that these statements are equivalent either to
B\Sigma^0_2 or to ACA_0 over the usual base system RCA_0.Comment: 8 pages, minor changes suggested by referee. To appear in MLQ -
Mathematical Logic Quarterl
Scott Ranks of Classifications of the Admissibility Equivalence Relation
Let be a recursive language. Let be the set of
-structures with domain . Let be a function with the property that
for all , if and only if
. Then there is some
so that
On structures in hypergraphs of models of a theory
We define and study structural properties of hypergraphs of models of a
theory including lattice ones. Characterizations for the lattice properties of
hypergraphs of models of a theory, as well as for structures on sets of
isomorphism types of models of a theory, are given
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