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 few results on the complexity of classes of identifiable recursive function sets
A few topological problems
A fine hierarchy of partition cardinals
A finitely Axiomatizable complete theory with atomless F1 (T).
A first order probability logic – .
A First-Order Conditional Probability Logic With Iterations
A first-order logic for multi-algebras.
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 equivalent to the axiom of choice.
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 forcing construction of thin-tall Boolean algebras
It was proved by Juhász and Weiss that for every ordinal α with there is a superatomic Boolean algebra of height α and width ω. We prove that if κ is an infinite cardinal such that and α is an ordinal such that , then there is a cardinal-preserving partial order that forces the existence of a superatomic Boolean algebra of height α and width κ. Furthermore, iterating this forcing through all , we obtain a notion of forcing that preserves cardinals and such that in the corresponding generic...
A formal analysis of musical scores
A formalization of the Lewis system S1 without rules of substitution.
In the Lewis and Langford formalization of system S1 (1932), besides the deduction rules, the substitution rules are as well used: the uniform substitution and the substitution of strict equivalents. They then obtain systems S2, S3, S4 and S5 adding to the axioms of S1 a new axiom, respectively, without changing the deduction rules. Lemmon (1957) gives a new formalization of systems S1-S5, calling them P1-P5. Is is worthwhile to remark that in the formalization of P2-P5 one does not use any more...
A free group of piecewise linear transformations
We prove the following conjecture of J. Mycielski: There exists a free nonabelian group of piecewise linear, orientation and area preserving transformations which acts on the punctured disk {(x,y) ∈ ℝ²: 0 < x² + y² < 1} without fixed points.
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.