A note on elementary end extension.
A note on embedding problems
A note on forking and normalization.
A note on generic subsets of definable groups
We generalize the theory of generic subsets of definably compact definable groups to arbitrary o-minimal structures. This theory is a crucial part of the solution to Pillay's conjecture connecting definably compact definable groups with Lie groups.
A note on infinite forcing.
A note on nonaxiomatizability of independence relations generated by certain probabilistic structures
A note on noninterpretability in o-minimal structures
We prove that if M is an o-minimal structure whose underlying order is dense then Th(M) does not interpret the theory of an infinite discretely ordered structure. We also make a conjecture concerning the class of the theory of an infinite discretely ordered o-minimal structure.
A note on Robinson's non-negativity criterion
A note on Steinhorn's omitting types theorem
Let p(x) be a nonprincipal type. We give a sufficient condition for a model M to have a proper elementary extension omitting p(x). As a corollary, we obtain a generalization of Steinhorn's omitting types theorem to the supersimple case.
A note on Sugihara algebras.
In [4] Blok and Pigozzi prove syntactically that RM, the propositional calculus also called R-Mingle, is algebraizable, and as a consequence there is a unique quasivariety (the so-called equivalent quasivariety semantics) associated to it. In [3] it is stated that this quasivariety is the variety of Sugihara algebras. Starting from this fact, in this paper we present an equational base for this variety obtained as a subvariety of the variety of R-algebras, found in [7] to be associated in the same...
A note on the Mac Dowell-Specker theorem
A Note on the two Cardinal Problem
A note on the two cardinal problem.
A Note on tight stable theories.
A note on topological model theory
A Note On Ultrapower Cardinality
A note on ultrapower cardinality.
A note on Δ₁ induction and Σ₁ collection
Slaman recently proved that Σₙ collection is provable from Δₙ induction plus exponentiation, partially answering a question of Paris. We give a new version of this proof for the case n = 1, which only requires the following very weak form of exponentiation: " exists for some y sufficiently large that x is smaller than some primitive recursive function of y".
A notion of functional completeness for first order structures. II: Quasiprimality.
A notion of functional completeness for first-order structure.