We add an analytic trans-exponential function $\varphi$ to $\mathbb{R}_{an,\exp}$. We reduce the o-minimality of $\mathbb{R}_{an,\exp,\varphi}$ to the existence of "many" regular values for some definable systems of functions, which is a necessary condition for the o-minimality of $\mathbb{R}_{an,\exp,\varphi}$.
We study some asymptotic variants of the club principle. Along the way, we construct some forcings and use them to separate several of these principles
We give an example of iteration of length omega of (<kappa)-complete kappa^+-cc forcing notions with the limit collapsing kappa^+. The construction is decoded from the proof of Shelah [Proper and Improper Forcing, Appendix, Theorem 3.6(1)].
Assume $\boldsymbolΔ^1_3$-determinacy. It is shown that for any $x \geq_T M_1^{\#}$, $\mathrm{HOD}^{L[x]}$ is a model of GCH, and in fact, it is a Jensen-Steel core model up to $ω_2^{L[x]}$.
We show that the countable universal omega-categorical bowtie-free graph admits generic automorphisms. Moreover, we show that this graph is not finitely homogenisable.
We give an algebro-geometric first-order axiomatization of DCF$_{0,m}$ (the theory of differentially closed fields of characteristic zero with m commuting derivations) in the spirit of the classical geometric axioms of DCF$_0$.
We show that a form of dependence known as G-dependence (originally introduced by Grelling) admits a very natural finite axiomatization, as well as Armstrong relations. We also give an explicit translation between functional dependence and G-dependence.
This article introduce a new model theory call non-predetermined model theory where functions and relations need not to be determined already and they are determined through time.
We continue our investigation on pcf with weak form of choice. Characteristically we assume DC + P(Y) when looking and prod_{s in Y} delta_s. We get more parallel of theorems on pcf.
We study and develop a notion of isogeny for superstable groups. We prove several fundamental properties of the notion and then use it to formulate and prove uniqueness results. Connections to existing model theoretic notions are explained.
We presents an independence relation on sets, one can define dimension by it, assuming that we have an abstract elementary class with a forking notion that satisfies the axioms of a good frame minus stability.
El hecho de que las palabras estén forjadas a partir de conceptos universales dificulta al lenguaje textual una relación precisa con la realidad material, en la medida que ésta es necesariamente particular y concreta. Por el contrario, el lenguaje gráfico se presta extraordinariamente bien a representar la realidad, a describirla con la mayor precisión dada su enorme capacidad de síntesis; funciona muy bien como verbalización de lo material. Tal vez por ello, en el proyecto de arquitectura, como documento legal que es, en el caso de discrepancia entre lo grafiado y lo descrito en la memoria o en las leyendas, prevalece lo primero. Así, somos capaces de figurar la realidad con gran exactitud y nivel de detalle gracias al dibujo precisamente porque la línea define de manera extraordinariamente sintética la proyección de formas geométricas sencillas –hasta hace muy poco casi la totalidad de las formas arquitectónicas-.
In Logic, non reflexivity translates into the absence of the identity axiom. This opens the field to the treatment of many language phenomena, like fallacies. Ludics, a frame invented by J-Y Girard, because it is founded on loci (adresses) and not on formulae, allows such a treatment.
We show that the supremum of the lengths of boldface Delta-1-2 prewellorderings of the reals can be Aleph-2, with Aleph-1 inac- cessible to reals, assuming only the consistency of an inaccessible.
We deal with stability theory for ``reasonable'' non-elementary classes without any remanents of compactness (like: above Hanf number or definable by L_{omega_1, omega}).