A characterization of expandability of models for ZF to models for KM
A characterization of Ext(G,ℤ) assuming (V = L)
We complete the characterization of Ext(G,ℤ) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence of cardinals satisfying (where Π is the set of all primes), there is a torsion-free abelian group G of size ν such that equals the p-rank of Ext(G,ℤ) for every...
A characterization of quasivarieties of partial algebras by means of limits and products.
A Completenes Theorem for an Infinitary Intutionistic Logic With Both Ordinary and Probability Quantifiers
A completeness theorem in the modal logic of programs
A Completness Theorem For One Class Of The Propositional Calculi
A decidable -categorical theory with a non-recursive Ryll-Nardzewski function
A decomposability criterion for elementary theories.
A decomposition of a set definable in an o-minimal structure into perfectly situated sets
A definable subset of a Euclidean space X is called perfectly situated if it can be represented in some linear system of coordinates as a finite union of (graphs of) definable 𝓒¹-maps with bounded derivatives. Two subsets of X are called simply separated if they satisfy the Łojasiewicz inequality with exponent 1. We show that every closed definable subset of X of dimension k can be decomposed into a finite family of closed definable subsets each of which is perfectly situated and such that any...
A deductive calculus for conditional equational systems with built-in predicates as premises.
A dichotomy theorem for mono-unary algebras
We study the isomorphism relation of invariant Borel classes of countable mono-unary algebras and prove a strong dichotomy theorem.
A failure of quantifier elimination.
We show that log is needed to eliminate quantifiers in the theory of the real numbers with restricted analytic functions and exponentiation.
A family of logarithmic functions of distinct growth rates
We construct a totally ordered set Γ of positive infinite germs (i.e. germs of positive real-valued functions that tend to +∞), with order type being the lexicographic product ℵ1 × ℤ2. We show that Γ admits order preserving automorphisms of pairwise distinct growth rates.
A few Remarks on n-infinite Forcing Companions
A few Remarks on Reduced Ideal-products
A finitely Axiomatizable complete theory with atomless F1 (T).
A first-order version of Pfaffian closure
The purpose of this paper is to extend a theorem of Speissegger [J. Reine Angew. Math. 508 (1999)], which states that the Pfaffian closure of an o-minimal expansion of the real field is o-minimal. Specifically, we display a collection of properties possessed by the real numbers that suffices for a version of the proof of this theorem to go through. The degree of flexibility revealed in this study permits the use of certain model-theoretic arguments for the first time, e.g. the compactness theorem....
A fixed point theorem in o-minimal structures
Here we prove an o-minimal fixed point theorem for definable continuous maps on definably compact definable sets, generalizing Brumfiel’s version of the Hopf fixed point theorem for semi-algebraic maps.
A fully equational proof of Parikh’s theorem
We show that the validity of Parikh’s theorem for context-free languages depends only on a few equational properties of least pre-fixed points. Moreover, we exhibit an infinite basis of -term equations of continuous commutative idempotent semirings.
A Fully Equational Proof of Parikh's Theorem
We show that the validity of Parikh's theorem for context-free languages depends only on a few equational properties of least pre-fixed points. Moreover, we exhibit an infinite basis of μ-term equations of continuous commutative idempotent semirings.