7 papers
A hyperamalgamation property
Paolo Lipparini
The superamalgamation property is a strengthening of the amalgamation property and has found many applications in algebraic logic, more recently, also in model theory. Here we intr…
Ordinal semigroups
Paolo Lipparini
In a previous paper we introduced a version of associativity for a partial infinitary operation. We prove here that if is an infinite ordinal and some associative infinitary o…
One-sided inverses in noncommutative infinitary semigroups
Paolo Lipparini
In a former paper we introduced partial infinitary noncommutative semigroups and showed, among other, that significant differences arise in comparison with the commutative case, pr…
Noncommutative infinitary semigroups
Paolo Lipparini
Various kinds of infinitary operations satisfying forms of associativity have been considered in the literature by various authors, including A. Tarski, C. Karp, J. H. Conway, D. K…
A Ring structure on the Class of Combinatorial Games
Harry Altman, Paolo Lipparini
J. Conway defined useful operations on the Class of combinatorial games and also introduced a notion of equivalence between games. Conway showed that, under his equivalence, games…
Monotone infinitary operations on ordinals (extended version)
Paolo Lipparini
We define and study an -ary operation on the class of the ordinals, which is strictly monotone in many significant cases (by an elementary argument, there is no fully strictly…