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.
A partial order where all monotone maps are definable
It is consistent that there is a partial order (P,≤) of size such that every monotone function f:P → P is first order definable in (P,≤).
A Possible Characterization of Generic Structures.
A proof of Saffe's conjecture
A proof of the valuation property and preparation theorem
The purpose of this article is to present a short model-theoretic proof of the valuation property for a polynomially bounded o-minimal theory T. The valuation property was conjectured by van den Dries, and proved for the polynomially bounded case by van den Dries-Speissegger and for the power bounded case by Tyne. Our proof uses the transfer principle for the theory (i.e. T with an extra unary symbol denoting a proper convex subring), which-together with quantifier elimination-is due to van den...
A property of stable theories
A property of the solvable radical in finitely decidable varieties
It is shown that in a finitely decidable equational class, the solvable radical of any finite subdirectly irreducible member is comparable to all congruences of the irreducible if the type of the monolith is 2. In the type 1 case we establish that the centralizer of the monolith is strongly solvable.
A propos d'un théorème de MacIntyre
A reflection phenomenon in descriptive set theory
A remark on accessible and axiomatizable categories
For categories with equalizers the concepts ``accessible'' and ``axiomatizable'' are equivalent. This results is proved under (in fact, is equivalent to) the large-cardinal Vopěnka's principle.
A remark on Ax's theorem on solvability modulo primes.