Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The strong amalgamation property into union   We consider the situation in which some class of structures has the Strong
Amalgamation Property (SAP) with the further requirement that the amalgamating
structure can be taken over the set theoretical union of (the images of) the
domains of the structures to be amalgamated. We call this property SAPU.
  The main advantage of SAPU over SAP is that there are many preservation
theorems showing that we can merge different theories with SAPU still obtaining
a theory with SAPU, hence with SAP. In particular, we elaborate on some
classical results by R. Fra\"iss\'e and B. J\'onsson, showing that any class of
partially ordered sets with a family of operators has SAPU.
  More generally, the argument applies to various theories with possibly many
binary relations and unary operations together, possibly satisfying some
coarseness, isotonicity and closure conditions. In particular, the theory of
two comparable binary relations has SAPU, where the relations can be chosen to
satisfy any range of properties among transitivity, reflexivity, symmetry,
antireflexivity, antisymmetry. In general, the result fails when three
relations are taken into account.
  SAPU is not limited to relational theories: the varieties defining the most
usual Maltsev conditions in universal algebra have SAPU. Other examples include
bounded directoids, order algebras and various generalization.

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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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