Related papers: Pure patterns of order 2
In the classification of real singularities by Arnold et al. (1985), normal forms, as representatives of equivalence classes under right equivalence, are not always uniquely determined. We describe the complete structure of the equivalence…
For every partial combinatory algebra (pca), we define a hierarchy of extensionality relations using ordinals. We investigate the closure ordinals of pca's, i.e. the smallest ordinals where these relations become equal. We show that the…
We present a general method for introducing finitely axiomatizable "minimal" two-sorted theories for various subclasses of P (problems solvable in polynomial time). The two sorts are natural numbers and finite sets of natural numbers. The…
A partial order is called semilinear iff the upper bounds of each element are linearly ordered and any two elements have a common upper bound. There exists, up to isomorphism, a unique countable existentially closed semilinear order, which…
Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of…
The paper is a first of two and aims to show that (assuming large cardinals) set theory is a tractable (and we dare to say tame) first order theory when formalized in a first order signature with natural predicate symbols for the basic…
The question of embedding fields into central simple algebras $B$ over a number field $K$ was the realm of class field theory. The subject of embedding orders contained in the ring of integers of maximal subfields $L$ of such an algebra…
Kruskal's theorem famously states that finite trees (ordered using an infima-preserving embeddability relation) form a well partial order. Freund, Rathjen, and Weiermann extended this result to general recursive data types with their…
Polar orderings arose in recent work of Salvetti and the second author on minimal CW-complexes for complexified hyperplane arrangements. We study the combinatorics of these orderings in the classical framework of oriented matroids, and…
We consider a slightly modified form of the standard Rudin-Keisler order on ideals and demonstrate the existence of complete (with respect to this order) ideals in various projective classes. Using our methods, we obtain a simple proof of…
Modal logic with propositional quantifiers (i.e. second-order propositional modal logic (SOPML)) has been considered since the early time of modal logic. Its expressive power and complexity are high, and its van-Benthem-Rosen theorem and…
Given a family $\F$ of posets closed under disjoint unions and the operation of taking convex subposets, we construct a category $\C_{\F}$ called the \emph{incidence category of $\F$}. This category is "nearly abelian" in the sense that all…
Several sequences of free cumulants that count binary plane trees correspond to sequences of classical cumulants that count the decreasing versions of the same trees. Using two new operations on colored binary plane trees that we call…
Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that…
We establish a categorical framework relating two canonical model constructions in first-order logic: the Henkin construction and compactness-based constructions via ultraproducts or saturation. By introducing a globally fixed set of Henkin…
Inspired by Leivant's work on absolute predicativism, Bellantoni and Cook in 1992 introduced a structurally restricted form of recursion called predicative recursion. Using this recursion scheme on the inductive structures of natural…
A sample of n generic points in the xy-plane defines a permutation that relates their ranks along the two axes. Every subset of k points similarly defines a pattern, which occurs in that permutation. The number of occurrences of small…
We define a new class of pushdown systems where the pushdown is a tree instead of a word. We allow a limited form of lookahead on the pushdown conforming to a certain ordering restriction, and we show that the resulting class enjoys a…
This dissertation is a contribution to the project of second-order set theory, which has seen a revival in recent years. The approach is to understand second-order set theory by studying the structure of models of second-order set theories.…
The theme of the first two sections, is to prepare the framework of how from a ``complicated'' family of so called index models $I \in K_1$ we build many and/or complicated structures in a class $K_2$. The index models are…